DEPARTMENT OF PHYSICS
DEPARTMENT OF PHYSICS 8.012 Physics I Prereq: None U (Fall) Undergraduate Subjects 5-0-7 units. PHYSICS I Credit cannot also be received for 8.01, 8.011, 8.01L, ES.801, ES.8012 8.01 Physics I Prereq: None Elementary mechanics, presented in greater depth than in 8.01. U (Fall) Newton's laws, concepts of momentum, energy, angular momentum, 3-2-7 units. PHYSICS I rigid body motion, and non-inertial systems. Uses elementary Credit cannot also be received for 8.011, 8.012, 8.01L, ES.801, calculus freely; concurrent registration in a math subject more ES.8012 advanced than 18.01 is recommended. In addition to covering the theoretical subject matter, students complete a small experimental Introduces classical mechanics. Space and time: straight-line project of their own design. Freshmen admitted via AP or Math kinematics; motion in a plane; forces and static equilibrium; particle Diagnostic for Physics Placement results. dynamics, with force and conservation of momentum; relative M. Soljacic inertial frames and non-inertial force; work, potential energy and conservation of energy; kinetic theory and the ideal gas; rigid bodies 8.01L Physics I and rotational dynamics; vibrational motion; conservation of angular Prereq: None momentum; central force motions; fluid mechanics. Subject taught U (Fall, IAP) using the TEAL (Technology-Enabled Active Learning) format which 3-2-7 units. PHYSICS I features students working in groups of three, discussing concepts, Credit cannot also be received for 8.01, 8.011, 8.012, ES.801, ES.8012 solving problems, and doing table-top experiments with the aid of computer data acquisition and analysis. Introduction to classical mechanics (see description under 8.01). J. Formaggio, P. Dourmashkin Includes components of the TEAL (Technology-Enabled Active Learning) format. Material covered over a longer interval so that the 8.011 Physics I subject is completed by the end of the IAP. Substantial emphasis Prereq: None given to reviewing and strengthening necessary mathematics U (Spring) tools, as well as basic physics concepts and problem-solving skills. 5-0-7 units. PHYSICS I Content, depth, and diculty is otherwise identical to that of 8.01. Credit cannot also be received for 8.01, 8.012, 8.01L, ES.801, The subject is designated as 8.01 on the transcript. ES.8012 P. Jarillo-Herrero
Introduces classical mechanics. Space and time: straight-line 8.02 Physics II kinematics; motion in a plane; forces and equilibrium; experimental Prereq: Calculus I (GIR) and Physics I (GIR) basis of Newton's laws; particle dynamics; universal gravitation; U (Fall, Spring) collisions and conservation laws; work and potential energy; 3-2-7 units. PHYSICS II vibrational motion; conservative forces; inertial forces and non- Credit cannot also be received for 8.021, 8.022, ES.802, ES.8022 inertial frames; central force motions; rigid bodies and rotational dynamics. Designed for students with previous experience in 8.01; Introduction to electromagnetism and electrostatics: electric the subject is designated as 8.01 on the transcript. charge, Coulomb's law, electric structure of matter; conductors D. Pritchard and dielectrics. Concepts of electrostatic eld and potential, electrostatic energy. Electric currents, magnetic elds and Ampere's law. Magnetic materials. Time-varying elds and Faraday's law of induction. Basic electric circuits. Electromagnetic waves and Maxwell's equations. Subject taught using the TEAL (Technology Enabled Active Learning) studio format which utilizes small group interaction and current technology to help students develop intuition about, and conceptual models of, physical phenomena. J. Belcher, I. Cisse
Department of Physics | 3 DEPARTMENT OF PHYSICS
8.021 Physics II 8.033 Relativity Prereq: Calculus I (GIR), Physics I (GIR), and permission of instructor Prereq: Calculus II (GIR) and Physics II (GIR) U (Fall) U (Fall) 5-0-7 units. PHYSICS II 5-0-7 units. REST Credit cannot also be received for 8.02, 8.022, ES.802, ES.8022 Einstein's postulates; consequences for simultaneity, time Introduction to electromagnetism and electrostatics: electric dilation, length contraction, and clock synchronization; Lorentz charge, Coulomb's law, electric structure of matter; conductors transformation; relativistic eects and paradoxes; Minkowski and dielectrics. Concepts of electrostatic eld and potential, diagrams; invariants and four-vectors; momentum, energy, and electrostatic energy. Electric currents, magnetic elds and Ampere's mass; particle collisions. Relativity and electricity; Coulomb's law. Magnetic materials. Time-varying elds and Faraday's law; magnetic elds. Brief introduction to Newtonian cosmology. law of induction. Basic electric circuits. Electromagnetic waves Introduction to some concepts of general relativity; principle of and Maxwell's equations. Designed for students with previous equivalence. The Schwarzchild metric; gravitational red shi; experience in 8.02; the subject is designated as 8.02 on the particle and light trajectories; geodesics; Shapiro delay. transcript. Enrollment limited. S. Vitale J. Checkelsky 8.04 Quantum Physics I 8.022 Physics II Prereq: 8.03 and (18.03 or 18.032) Prereq: Physics I (GIR); Coreq: Calculus II (GIR) U (Spring) U (Fall, Spring) 5-0-7 units. REST 5-0-7 units. PHYSICS II Credit cannot also be received for 8.041 Credit cannot also be received for 8.02, 8.021, ES.802, ES.8022 Experimental basis of quantum physics: photoelectric eect, Parallel to 8.02, but more advanced mathematically. Some Compton scattering, photons, Franck-Hertz experiment, the Bohr knowledge of vector calculus assumed. Maxwell's equations, in atom, electron diraction, deBroglie waves, and wave-particle both dierential and integral form. Electrostatic and magnetic duality of matter and light. Introduction to wave mechanics: vector potential. Properties of dielectrics and magnetic materials. Schroedinger's equation, wave functions, wave packets, probability In addition to the theoretical subject matter, several experiments amplitudes, stationary states, the Heisenberg uncertainty principle, in electricity and magnetism are performed by the students in the and zero-point energies. Solutions to Schroedinger's equation in laboratory. one dimension: transmission and reflection at a barrier, barrier D. Harlow penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials and 8.03 Physics III introduction to hydrogenic systems. Prereq: Calculus II (GIR) and Physics II (GIR) V. Vuletic U (Fall, Spring) 5-0-7 units. REST
Mechanical vibrations and waves; simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations, and normal modes; vibrations of continuous systems; reflection and refraction; phase and group velocity. Optics; wave solutions to Maxwell's equations; polarization; Snell's Law, interference, Huygens's principle, Fraunhofer diraction, and gratings. Y-J. Lee, R. Comin
4 | Department of Physics DEPARTMENT OF PHYSICS
8.041 Quantum Physics I (New) 8.05 Quantum Physics II Prereq: 8.03 and (18.03 or 18.032) Prereq: 8.04 U (Fall) U (Fall) 2-0-10 units. REST 5-0-7 units Credit cannot also be received for 8.04 Credit cannot also be received for 8.051
Blended version of 8.04 using a combination of online and in- Together 8.05 and 8.06 cover quantum physics with applications person instruction. Covers experimental basis of quantum physics: drawn from modern physics. General formalism of quantum photoelectric eect, Compton scattering, photons, Franck-Hertz mechanics: states, operators, Dirac notation, representations, experiment, the Bohr atom, electron diraction, deBroglie waves, measurement theory. Harmonic oscillator: operator algebra, states. and wave-particle duality of matter and light. Introduction to wave Quantum mechanics in three dimensions: central potentials and the mechanics: Schroedinger's equation, wave functions, wave packets, radial equation, bound and scattering states, qualitative analysis of probability amplitudes, stationary states, the Heisenberg uncertainty wavefunctions. Angular momentum: operators, commutator algebra, principle, and zero-point energies. Solutions to Schroedinger's eigenvalues and eigenstates, spherical harmonics. Spin: Stern- equation in one dimension: transmission and reflection at a barrier, Gerlach devices and measurements, nuclear magnetic resonance, barrier penetration, potential wells, the simple harmonic oscillator. spin and statistics. Addition of angular momentum: Clebsch-Gordan Schroedinger's equation in three dimensions: central potentials and series and coecients, spin systems, and allotropic forms of introduction to hydrogenic systems. hydrogen. V. Vuletic W. Detmold
8.044 Statistical Physics I 8.051 Quantum Physics II Prereq: 8.03 and 18.03 Prereq: 8.04 and permission of instructor U (Spring) U (Spring) 5-0-7 units 2-0-10 units Credit cannot also be received for 8.05 Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional Blended version of 8.05 using a combination of online and probability densities, and functions of a random variable. Concepts in-person instruction. Together with 8.06 covers quantum of macroscopic variables and thermodynamic equilibrium, physics with applications drawn from modern physics. General fundamental assumption of statistical mechanics, microcanonical formalism of quantum mechanics: states, operators, Dirac and canonical ensembles. First, second, and third laws of notation, representations, measurement theory. Harmonic thermodynamics. Numerous examples illustrating a wide variety of oscillator: operator algebra, states. Quantum mechanics in three physical phenomena such as magnetism, polyatomic gases, thermal dimensions: central potentials and the radial equation, bound and radiation, electrons in solids, and noise in electronic devices. scattering states, qualitative analysis of wave functions. Angular Concurrent enrollment in 8.04 is recommended. momentum: operators, commutator algebra, eigenvalues and N. Fakhri eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coecients, spin systems, and allotropic forms of hydrogen. Limited to 20. Fall: Sta Spring: W. Detmold
Department of Physics | 5 DEPARTMENT OF PHYSICS
8.06 Quantum Physics III 8.09 Classical Mechanics III Prereq: 8.05 Subject meets with 8.309 U (Spring) Prereq: 8.223 5-0-7 units U (Fall) 4-0-8 units Continuation of 8.05. Units: natural units, scales of microscopic phenomena, applications. Time-independent approximation Covers Lagrangian and Hamiltonian mechanics, systems with methods: degenerate and nondegenerate perturbation theory, constraints, rigid body dynamics, vibrations, central forces, variational method, Born-Oppenheimer approximation, applications Hamilton-Jacobi theory, action-angle variables, perturbation to atomic and molecular systems. The structure of one- and two- theory, and continuous systems. Provides an introduction to ideal electron atoms: overview, spin-orbit and relativistic corrections, and viscous fluid mechanics, including turbulence, as well as an ne structure, variational approximation, screening, Zeeman and introduction to nonlinear dynamics, including chaos. Students taking Stark eects. Charged particles in a magnetic eld: Landau levels graduate version complete dierent assignments. and integer quantum hall eect. Scattering: general principles, I. Stewart partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation. Time-dependent perturbation Undergraduate Laboratory and Special Project Subjects theory. Students research and write a paper on a topic related to the content of 8.05 and 8.06. 8.10 Exploring and Communicating Physics (and other) Frontiers B. Zwiebach Prereq: None U (Fall) 8.07 Electromagnetism II 2-0-0 units Prereq: 8.03 and 18.03 U (Fall) Features a series of 12 interactive sessions that span a wide variety 4-0-8 units of topics at the frontiers of science - e.g., quantum computing, dark matter, the nature of time - and encourage independent Survey of basic electromagnetic phenomena: electrostatics, thinking. Discussions draw from the professor's published pieces in magnetostatics; electromagnetic properties of matter. Time- periodicals as well as short excerpts from his books. Also discusses, dependent electromagnetic elds and Maxwell's equations. through case studies, the process of writing and re-writing. Subject Electromagnetic waves, emission, absorption, and scattering of can count toward the 6-unit discovery-focused credit limit for rst radiation. Relativistic electrodynamics and mechanics. year students. A. Guth F. Wilczek
8.08 Statistical Physics II 8.13 Experimental Physics I Prereq: 8.044 and 8.05 Prereq: 8.04 U (Spring) U (Fall, Spring) 4-0-8 units 0-6-12 units. Institute LAB
Probability distributions for classical and quantum systems. Four fundamental laboratory experiments are carried out each term, Microcanonical, canonical, and grand canonical partition- covering most aspects of modern physics relating to names such functions and associated thermodynamic potentials. Conditions as Rutherford, Franck-Hertz, Hall, Ramsauer, Doppler, Fraunhofer, of thermodynamic equilibrium for homogenous and heterogenous Faraday, Mossbauer, Compton, and Stern-Gerlach. Stresses basic systems. Applications: non-interacting Bose and Fermi gases; experimental techniques and data analysis, and written and oral mean eld theories for real gases, binary mixtures, magnetic presentation of experiment results. systems, polymer solutions; phase and reaction equilibria, critical J. Conrad, J. Formaggio, A. Levine, K. Perez phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations. Fall: Sta Spring: L. Fu
6 | Department of Physics DEPARTMENT OF PHYSICS
8.14 Experimental Physics II Undergraduate Elective Subjects Prereq: 8.05 and 8.13 U (Spring) 8.20 Introduction to Special Relativity 0-6-12 units Prereq: Calculus I (GIR) and Physics I (GIR) Four fundamental laboratory experiments are carried out each term, U (IAP) covering most aspects of modern physics relating to names such 2-0-7 units. REST as Rutherford, Franck-Hertz, Hall, Ramsauer, Doppler, Fraunhofer, Introduces the basic ideas and equations of Einstein's special Faraday, Mossbauer, Compton, and Stern-Gerlach. Stresses basic theory of relativity. Topics include Lorentz transformations, length experimental techniques and data analysis, and written and oral contraction and time dilation, four vectors, Lorentz invariants, presentation of experiment results. 8.14 requires knowledge of relativistic energy and momentum, relativistic kinematics, Doppler quantum mechanics at the 8.05 level. shi, space-time diagrams, relativity paradoxes, and some concepts G. Roland of general relativity. Intended for freshmen and sophomores. Not usable as a restricted elective by Physics majors. Credit cannot be 8.18 Research Problems in Undergraduate Physics received for 8.20 if credit for 8.033 is or has been received in the Prereq: Permission of instructor same or prior terms. U (Fall, IAP, Spring, Summer) S. Vitale Units arranged [P/D/F] Can be repeated for credit. 8.21 Physics of Energy Opportunity for undergraduates to engage in experimental or Prereq: Calculus II (GIR), Chemistry (GIR), and Physics II (GIR) theoretical research under the supervision of a sta member. U (Spring) Specic approval required in each case. 5-0-7 units. REST Consult N. Mavalvala A comprehensive introduction to the fundamental physics of energy systems that emphasizes quantitative analysis. Focuses on the 8.19 Readings in Physics fundamental physical principles underlying energy processes and on Prereq: None the application of these principles to practical calculations. Applies U (Fall, IAP, Spring, Summer) mechanics and electromagnetism to energy systems; introduces and Units arranged [P/D/F] applies basic ideas from thermodynamics, quantum mechanics, and Can be repeated for credit. nuclear physics. Examines energy sources, conversion, transport, Supervised reading and library work. Choice of material and losses, storage, conservation, and end uses. Analyzes the physics of allotment of time according to individual needs. For students who side eects, such as global warming and radiation hazards. Provides want to do work not provided for in the regular subjects. Specic students with technical tools and perspective to evaluate energy approval required in each case. choices quantitatively at both national policy and personal levels. Consult N. Mavalvala R. Jae
8.223 Classical Mechanics II Prereq: Calculus II (GIR) and Physics I (GIR) U (IAP) 2-0-4 units
A broad, theoretical treatment of classical mechanics, useful in its own right for treating complex dynamical problems, but essential to understanding the foundations of quantum mechanics and statistical physics. Generalized coordinates, Lagrangian and Hamiltonian formulations, canonical transformations, and Poisson brackets. Applications to continuous media. The relativistic Lagrangian and Maxwell's equations. Sta, M. Evans
Department of Physics | 7 DEPARTMENT OF PHYSICS
8.224 Exploring Black Holes: General Relativity and 8.231 Physics of Solids I Astrophysics Prereq: 8.044; Coreq: 8.05 Prereq: 8.033 or 8.20 U (Fall) Acad Year 2021-2022: Not oered 4-0-8 units Acad Year 2022-2023: U (Fall) 3-0-9 units Introduction to the basic concepts of the quantum theory of solids. Topics: periodic structure and symmetry of crystals; diraction; Study of physical eects in the vicinity of a black hole as a basis reciprocal lattice; chemical bonding; lattice dynamics, phonons, for understanding general relativity, astrophysics, and elements thermal properties; free electron gas; model of metals; Bloch of cosmology. Extension to current developments in theory and theorem and band structure, nearly free electron approximation; observation. Energy and momentum in flat space-time; the metric; tight binding method; Fermi surface; semiconductors, electrons, curvature of space-time near rotating and nonrotating centers of holes, impurities; optical properties, excitons; and magnetism. attraction; trajectories and orbits of particles and light; elementary S. Todadri models of the Cosmos. Weekly meetings include an evening seminar and recitation. The last third of the term is reserved for collaborative 8.241 Introduction to Biological Physics research projects on topics such as the Global Positioning System, Prereq: Physics II (GIR) and (5.60 or 8.044) solar system tests of relativity, descending into a black hole, U (Spring) gravitational lensing, gravitational waves, Gravity Probe B, and more 4-0-8 units advanced models of the cosmos. Subject has online components Credit cannot also be received for 20.315, 20.415 that are open to selected MIT alumni. Alumni wishing to participate should contact Professor Bertschinger at [email protected]. Limited to Introduces the main concepts of biological physics, with a focus 40. on biophysical phenomena at the molecular and cellular scales. E. Bertschinger Presents the role of entropy and diusive transport in living matter; challenges to life resulting from the highly viscous environment 8.225[J] Einstein, Oppenheimer, Feynman: Physics in the 20th present at microscopic scales, including constraints on force, Century motion and transport within cells, tissues, and fluids; principles Same subject as STS.042[J] of how cellular machinery (e.g., molecular motors) can convert Prereq: None electro-chemical energy sources to mechanical forces and motion. Acad Year 2021-2022: Not oered Also covers polymer physics relevant to DNA and other biological Acad Year 2022-2023: U (Fall) polymers, including the study of congurations, fluctuations, 3-0-9 units. HASS-H rigidity, and entropic elasticity. 20.315 and 20.415 meet with 8.241 when oered concurrently. See description under subject STS.042[J]. Enrollment limited. I. Cisse D. I. Kaiser 8.245[J] Viruses, Pandemics, and Immunity 8.226 Forty-three Orders of Magnitude Same subject as 5.003[J], 10.382[J], HST.439[J] Prereq: (8.04 and 8.044) or permission of instructor Subject meets with 5.002[J], 10.380[J], HST.438[J] U (Spring) Prereq: None Not oered regularly; consult department U (Spring) 3-0-9 units 2-0-1 units
Examines the widespread societal implications of current scientic See description under subject HST.439[J]. HST.438[J] intended for discoveries in physics across forty-three orders of magnitude in rst-year students; all others should take HST.439[J]. length scale. Addresses topics ranging from climate change to A. Chakraborty nuclear nonproliferation. Students develop their ability to express concepts at a level accessible to the public and to present a well- reasoned argument on a topic that is a part of the national debate. Requires diverse writing assignments, including substantial papers. Enrollment limited. J. Conrad
8 | Department of Physics DEPARTMENT OF PHYSICS
8.251 String Theory for Undergraduates 8.282[J] Introduction to Astronomy Prereq: 8.033, 8.044, and 8.05 Same subject as 12.402[J] Acad Year 2021-2022: Not oered Prereq: Physics I (GIR) Acad Year 2022-2023: U (Spring) U (Spring) 4-0-8 units 3-0-6 units. REST Credit cannot also be received for 8.821 Quantitative introduction to the physics of planets, stars, galaxies Introduction to the main concepts of string theory, i.e., quantum and our universe, from origin to ultimate fate, with emphasis mechanics of a relativistic string. Develops aspects of string on the physics tools and observational techniques that enable theory and makes it accessible to students familiar with basic our understanding. Topics include our solar system, extrasolar electromagnetism and statistical mechanics, including the study of planets; our Sun and other "normal" stars, star formation, evolution D-branes and string thermodynamics. Meets with 8.821 when oered and death, supernovae, compact objects (white dwarfs, neutron concurrently. stars, pulsars, stellar-mass black holes); galactic structure, star H. Liu clusters, interstellar medium, dark matter; other galaxies, quasars, supermassive black holes, gravitational waves; cosmic large-scale 8.276 Nuclear and Particle Physics structure, origin, evolution and fate of our universe, inflation, dark Prereq: 8.033 and 8.04 energy, cosmic microwave background radiation, gravitational U (Spring) lensing, 21cm tomography. Not usable as a restricted elective by Not oered regularly; consult department Physics majors. 4-0-8 units M. Tegmark
Presents a modern view of the fundamental structure of matter. 8.284 Modern Astrophysics Starting from the Standard Model, which views leptons and quarks Prereq: 8.04; Coreq: 8.05 as basic building blocks of matter, establishes the properties U (Spring) and interactions of these particles. Explores applications of this 3-0-9 units phenomenology to both particle and nuclear physics. Emphasizes current topics in nuclear and particle physics research at MIT. Applications of physics (Newtonian, statistical, and quantum Intended for students with a basic knowledge of relativity and mechanics) to fundamental processes that occur in celestial objects. quantum physics concepts. Includes main-sequence stars, collapsed stars (white dwarfs, M. Williams neutron stars, and black holes), pulsars, supernovae, the interstellar medium, galaxies, and as time permits, active galaxies, quasars, and 8.277 Introduction to Particle Accelerators cosmology. Observational data discussed. No prior knowledge of Prereq: (6.013 or 8.07) and permission of instructor astronomy is required. U (Fall, IAP, Spring) N. Weinberg Not oered regularly; consult department Units arranged 8.286 The Early Universe Can be repeated for credit. Prereq: Physics II (GIR) and 18.03 Acad Year 2021-2022: Not oered Principles of acceleration: beam properties; linear accelerators, Acad Year 2022-2023: U (Fall) synchrotrons, and storage rings. Accelerator technologies: 3-0-9 units. REST radio frequency cavities, bending and focusing magnets, beam diagnostics. Particle beam optics and dynamics. Special topics: Introduction to modern cosmology. First half deals with the measures of accelerators performance in science, medicine and development of the big bang theory from 1915 to 1980, and latter half industry; synchrotron radiation sources; free electron lasers; high- with recent impact of particle theory. Topics: special relativity and energy colliders; and accelerators for radiation therapy. May be the Doppler eect, Newtonian cosmological models, introduction repeated for credit for a maximum of 12 units. to non-Euclidean spaces, thermal radiation and early history of W. Barletta the universe, big bang nucleosynthesis, introduction to grand unied theories and other recent developments in particle theory, baryogenesis, the inflationary universe model, and the evolution of galactic structure. A. Guth
Department of Physics | 9 DEPARTMENT OF PHYSICS
8.287[J] Observational Techniques of Optical Astronomy 8.295 Practical Experience in Physics Same subject as 12.410[J] Prereq: None Prereq: 8.282[J], 12.409, or other introductory astronomy course U (Fall, IAP, Spring, Summer) U (Fall) 0-1-0 units 3-4-8 units. Institute LAB Can be repeated for credit.
See description under subject 12.410[J]. Limited to 18; preference to For Course 8 students participating in o-campus experiences in Course 8 and Course 12 majors and minors. physics. Before registering for this subject, students must have an R. Binzel, A. Bosh internship oer from a company or organization and must identify a Physics supervisor. Upon completion of the project, student must 8.290[J] Extrasolar Planets: Physics and Detection Techniques submit a letter from the company or organization describing the work Same subject as 12.425[J] accomplished, along with a substantive nal report from the student Subject meets with 12.625 approved by the MIT supervisor. Subject to departmental approval. Prereq: 8.03 and 18.03 Consult departmental academic oce. U (Fall) Consult N. Mavalvala 3-0-9 units. REST 8.298 Selected Topics in Physics See description under subject 12.425[J]. Prereq: Permission of instructor S. Seager U (Fall, IAP, Spring, Summer) Units arranged 8.292[J] Fluid Physics Can be repeated for credit. Same subject as 12.330[J] Prereq: 5.60, 8.044, or permission of instructor Presentation of topics of current interest, with content varying from U (Spring) year to year. Not oered regularly; consult department Consult I. Stewart 3-0-9 units 8.299 Physics Teaching A physics-based introduction to the properties of fluids and fluid Prereq: None systems, with examples drawn from a broad range of sciences, U (Fall, Spring) including atmospheric physics and astrophysics. Denitions Units arranged [P/D/F] of fluids and the notion of continuum. Equations of state and Can be repeated for credit. continuity, hydrostatics and conservation of momentum; ideal fluids and Euler's equation; viscosity and the Navier-Stokes equation. For qualied undergraduate students interested in gaining some Energy considerations, fluid thermodynamics, and isentropic experience in teaching. Laboratory, tutorial, or classroom teaching flow. Compressible versus incompressible and rotational versus under the supervision of a faculty member. Students selected by irrotational flow; Bernoulli's theorem; steady flow, streamlines and interview. potential flow. Circulation and vorticity. Kelvin's theorem. Boundary Consult N. Mavalvala layers. Fluid waves and instabilities. Quantum fluids. Sta 8.EPE UPOP Engineering Practice Experience Engineering School-Wide Elective Subject. Oered under: 1.EPE, 2.EPE, 3.EPE, 6.EPE, 8.EPE, 10.EPE, 15.EPE, 16.EPE, 20.EPE, 22.EPE Prereq: 2.EPW or permission of instructor U (Fall, Spring) 0-0-1 units
See description under subject 2.EPE. Sta
10 | Department of Physics DEPARTMENT OF PHYSICS
8.S10 Special Subject: Physics 8.THU Undergraduate Physics Thesis Prereq: None Prereq: None U (Spring) U (Fall, IAP, Spring, Summer) Units arranged Units arranged Can be repeated for credit. Can be repeated for credit.
Opportunity for group study of subjects in physics not otherwise Program of research leading to the writing of an S.B. thesis; to be included in the curriculum. arranged by the student under approved supervision. A. Adams, K. Ellenbogen Information: N. Mavalvala
8.S227 Special Subject: Physics Graduate Subjects Prereq: None U (Spring) 8.309 Classical Mechanics III 3-0-9 units Subject meets with 8.09 Opportunity for group study of subjects in physics not otherwise Prereq: None included in the curriculum. G (Fall) R. Price 4-0-8 units Covers Lagrangian and Hamiltonian mechanics, systems with 8.S30 Special Subject: Physics constraints, rigid body dynamics, vibrations, central forces, Prereq: None Hamilton-Jacobi theory, action-angle variables, perturbation U (IAP) theory, and continuous systems. Provides an introduction to ideal Not oered regularly; consult department and viscous fluid mechanics, including turbulence, as well as an Units arranged introduction to nonlinear dynamics, including chaos. Students taking Opportunity for group study of subjects in physics not otherwise graduate version complete dierent assignments. included in the curriculum. I. Stewart A. Bernstein, J. Walsh 8.311 Electromagnetic Theory I 8.S50 Special Subject: Physics Prereq: 8.07 Prereq: None G (Spring) U (IAP) 4-0-8 units Units arranged [P/D/F] Basic principles of electromagnetism: experimental basis, Can be repeated for credit. electrostatics, magnetic elds of steady currents, motional emf and Opportunity for group study of subjects in physics not otherwise electromagnetic induction, Maxwell's equations, propagation and included in the curriculum. radiation of electromagnetic waves, electric and magnetic properties E. Bertschinger of matter, and conservation laws. Subject uses appropriate mathematics but emphasizes physical phenomena and principles. 8.UR Undergraduate Research J. Belcher Prereq: None U (Fall, IAP, Spring, Summer) 8.315[J] Mathematical Methods in Nanophotonics Units arranged [P/D/F] Same subject as 18.369[J] Can be repeated for credit. Prereq: 8.07, 18.303, or permission of instructor Acad Year 2021-2022: G (Fall) Research opportunities in physics. For further information, contact Acad Year 2022-2023: Not oered the departmental UROP coordinator. 3-0-9 units N. Mavalvala See description under subject 18.369[J]. S. G. Johnson
Department of Physics | 11 DEPARTMENT OF PHYSICS
8.321 Quantum Theory I 8.324 Relativistic Quantum Field Theory II Prereq: 8.05 Prereq: 8.322 and 8.323 G (Fall) G (Fall) 4-0-8 units 4-0-8 units
A two-term subject on quantum theory, stressing principles: The second term of the quantum eld theory sequence. Develops uncertainty relation, observables, eigenstates, eigenvalues, in depth some of the topics discussed in 8.323 and introduces probabilities of the results of measurement, transformation theory, some advanced material. Topics: perturbation theory and Feynman equations of motion, and constants of motion. Symmetry in quantum diagrams, scattering theory, Quantum Electrodynamics, one loop mechanics, representations of symmetry groups. Variational and renormalization, quantization of non-abelian gauge theories, the perturbation approximations. Systems of identical particles and Standard Model of particle physics, other topics. applications. Time-dependent perturbation theory. Scattering T. Slatyer theory: phase shis, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic 8.325 Relativistic Quantum Field Theory III quantum mechanics of one electron. Prereq: 8.324 H. Liu G (Spring) 4-0-8 units 8.322 Quantum Theory II Prereq: 8.07 and 8.321 The third and last term of the quantum eld theory sequence. Its aim Acad Year 2021-2022: G (Spring) is the proper theoretical discussion of the physics of the standard Acad Year 2022-2023: Not oered model. Topics: quantum chromodynamics; Higgs phenomenon 4-0-8 units and a description of the standard model; deep-inelastic scattering and structure functions; basics of lattice gauge theory; operator A two-term subject on quantum theory, stressing principles: products and eective theories; detailed structure of the standard uncertainty relation, observables, eigenstates, eigenvalues, model; spontaneously broken gauge theory and its quantization; probabilities of the results of measurement, transformation theory, instantons and theta-vacua; topological defects; introduction to equations of motion, and constants of motion. Symmetry in quantum supersymmetry. mechanics, representations of symmetry groups. Variational and W. Taylor perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering 8.333 Statistical Mechanics I theory: phase shis, Born approximation. The quantum theory of Prereq: 8.044 and 8.05 radiation. Second quantization and many-body theory. Relativistic G (Fall) quantum mechanics of one electron. 4-0-8 units S. Todadri First part of a two-subject sequence on statistical mechanics. 8.323 Relativistic Quantum Field Theory I Examines the laws of thermodynamics and the concepts of Prereq: 8.321 temperature, work, heat, and entropy. Postulates of classical G (Spring) statistical mechanics, microcanonical, canonical, and grand 4-0-8 units canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose A one-term self-contained subject in quantum eld theory. Concepts systems. Interacting systems: cluster expansions, van der Waal's and basic techniques are developed through applications in gas, and mean-eld theory. elementary particle physics, and condensed matter physics. M. Kardar Topics: classical eld theory, symmetries, and Noether's theorem. Quantization of scalar elds, spin elds, and Gauge bosons. Feynman graphs, analytic properties of amplitudes and unitarity of the S-matrix. Calculations in quantum electrodynamics (QED). Introduction to renormalization. T. Slatyer
12 | Department of Physics DEPARTMENT OF PHYSICS
8.334 Statistical Mechanics II 8.371[J] Quantum Information Science Prereq: 8.333 Same subject as 6.443[J], 18.436[J] Acad Year 2021-2022: Not oered Prereq: 18.435[J] Acad Year 2022-2023: G (Spring) G (Spring) 4-0-8 units 3-0-9 units
Second part of a two-subject sequence on statistical mechanics. Examines quantum computation and quantum information. Topics Explores topics from modern statistical mechanics: the include quantum circuits, the quantum Fourier transform and hydrodynamic limit and classical eld theories. Phase transitions search algorithms, the quantum operations formalism, quantum and broken symmetries: universality, correlation functions, error correction, Calderbank-Shor-Steane and stabilizer codes, and scaling theory. The renormalization approach to collective fault tolerant quantum computation, quantum data compression, phenomena. Dynamic critical behavior. Random systems. quantum entanglement, capacity of quantum channels, and quantum Sta cryptography and the proof of its security. Prior knowledge of quantum mechanics required. 8.351[J] Classical Mechanics: A Computational Approach I. Chuang, A. Harrow Same subject as 6.946[J], 12.620[J] Prereq: Physics I (GIR), 18.03, and permission of instructor 8.381, 8.382 Selected Topics in Theoretical Physics Acad Year 2021-2022: Not oered Prereq: Permission of instructor Acad Year 2022-2023: G (Fall) G (Fall, Spring) 3-3-6 units Not oered regularly; consult department 3-0-9 units See description under subject 12.620[J]. J. Wisdom, G. J. Sussman Topics of current interest in theoretical physics, varying from year to year. Subject not routinely oered; given when sucient interest is 8.361 Quantum Theory of Many-Particle Systems indicated. Prereq: 8.322 and 8.333 Sta G (Fall) Not oered regularly; consult department 8.391 Pre-Thesis Research 3-0-9 units Prereq: Permission of instructor G (Fall) Introduces general many-body theory applicable to low temperature, Units arranged [P/D/F] nuclear, and solid-state physics. Reviews occupation number Can be repeated for credit. representation and classical Mayer expansion. Perturbation theory: diagrammatic expansions and linked-cluster theorem for zero or Advanced problems in any area of experimental or theoretical nite temperature systems of fermions or bosons. Green's functions: physics, with assigned reading and consultations. analytic properties, equations of motion, relation to observables, Sta approximations, linear response theory, and random phase approximation. Superconductivity: electron-phonon interaction, 8.392 Pre-Thesis Research instability of normal state, BCS ground state, perturbation theory. Prereq: Permission of instructor Sta G (Spring, Summer) Units arranged [P/D/F] 8.370[J] Quantum Computation Can be repeated for credit. Same subject as 2.111[J], 18.435[J] Prereq: 8.05, 18.06, 18.061, 18.700, or 18.701 Advanced problems in any area of experimental or theoretical G (Fall) physics, with assigned reading and consultations. 3-0-9 units Sta
See description under subject 18.435[J]. I. Chuang, A. Harrow, S. Lloyd, P. Shor
Department of Physics | 13 DEPARTMENT OF PHYSICS
8.395[J] Teaching College-Level Science and Engineering 8.422 Atomic and Optical Physics II Same subject as 1.95[J], 5.95[J], 7.59[J], 18.094[J] Prereq: 8.05 Subject meets with 2.978 Acad Year 2021-2022: Not oered Prereq: None Acad Year 2022-2023: G (Spring) G (Fall) 3-0-9 units 2-0-2 units The second of a two-term subject sequence that provides the See description under subject 5.95[J]. foundations for contemporary research in selected areas of atomic J. Rankin and optical physics. Non-classical states of light- squeezed states; multi-photon processes, Raman scattering; coherence- level 8.398 Selected Topics in Graduate Physics crossings, quantum beats, double resonance, superradiance; Prereq: None trapping and cooling- light forces, laser cooling, atom optics, G (Fall, Spring) spectroscopy of trapped atoms and ions; atomic interactions- Units arranged classical collisions, quantum scattering theory, ultracold collisions; Can be repeated for credit. and experimental methods. Sta A seminar for rst-year PhD students presenting topics of current interest, with content varying from year to year. Open only to rst- 8.431[J] Nonlinear Optics year graduate students in Physics. Same subject as 6.634[J] Consult J. Thaler Prereq: 6.013 or 8.07 G (Spring) 8.399 Physics Teaching 3-0-9 units Prereq: Permission of instructor G (Fall, Spring) See description under subject 6.634[J]. Units arranged [P/D/F] J. G. Fujimoto Can be repeated for credit. 8.481, 8.482 Selected Topics in Physics of Atoms and Radiation For qualied graduate students interested in gaining some Prereq: 8.321 experience in teaching. Laboratory, tutorial, or classroom teaching G (Fall, Spring) under the supervision of a faculty member. Students selected by Not oered regularly; consult department interview. 3-0-9 units Consult C. Paus Presentation of topics of current interest, with content varying from Physics of Atoms, Radiation, Solids, Fluids, and Plasmas year to year. Subject not routinely oered; given when sucient interest is indicated. 8.421 Atomic and Optical Physics I Sta Prereq: 8.05 Acad Year 2021-2022: G (Spring) 8.511 Theory of Solids I Acad Year 2022-2023: Not oered Prereq: 8.231 3-0-9 units G (Fall) 3-0-9 units The rst of a two-term subject sequence that provides the foundations for contemporary research in selected areas of atomic First term of a theoretical treatment of the physics of solids. Concept and optical phsyics. The interaction of radiation with atoms: of elementary excitations. Symmetry- translational, rotational, and resonance; absorption, stimulated and spontaneous emission; time-reversal invariances- theory of representations. Energy bands- methods of resonance, dressed atom formalism, masers and lasers, electrons and phonons. Topological band theory. Survey of electronic cavity quantum electrodynamics; structure of simple atoms, behavior structure of metals, semimetals, semiconductors, and insulators, in very strong elds; fundamental tests: time reversal, parity excitons, critical points, response functions, and interactions in the violations, Bell's inequalities; and experimental methods. electron gas. Theory of superconductivity. M. Zwierlein L. Levitov
14 | Department of Physics DEPARTMENT OF PHYSICS
8.512 Theory of Solids II 8.581, 8.582 Selected Topics in Condensed Matter Physics Prereq: 8.511 Prereq: Permission of instructor G (Spring) Acad Year 2021-2022: Not oered 3-0-9 units Acad Year 2022-2023: G (Spring) 3-0-9 units Second term of a theoretical treatment of the physics of solids. Can be repeated for credit. Interacting electron gas: many-body formulation, Feynman diagrams, random phase approximation and beyond. General Presentation of topics of current interest, with contents varying from theory of linear response: dielectric function; sum rules; plasmons; year to year. Subject not routinely oered; given when sucient optical properties; applications to semiconductors, metals, and interest is indicated. insulators. Transport properties: non-interacting electron gas Sta with impurities, diusons. Quantum Hall eect: integral and fractional. Electron-phonon interaction: general theory, applications 8.590[J] Topics in Biophysics and Physical Biology to metals, semiconductors and insulators, polarons, and eld- Same subject as 7.74[J], 20.416[J] theory description. Superconductivity: experimental observations, Prereq: None phenomenological theories, and BCS theory. G (Fall) L. Levitov Not oered regularly; consult department 2-0-4 units 8.513 Many-Body Theory for Condensed Matter Systems Prereq: 8.033, 8.05, 8.08, and 8.231 See description under subject 20.416[J]. Acad Year 2021-2022: G (Fall) I. Cisse, N. Fakhri, M. Guo Acad Year 2022-2023: Not oered 3-0-9 units 8.591[J] Systems Biology Same subject as 7.81[J] Concepts and physical pictures behind various phenomena that Subject meets with 7.32 appear in interacting many-body systems. Visualization occurs Prereq: (18.03 and 18.05) or permission of instructor through concentration on path integral, mean-eld theories and G (Fall) semiclassical picture of fluctuations around mean-eld state. Topics 3-0-9 units covered: interacting boson/fermion systems, Fermi liquid theory and bosonization, symmetry breaking and nonlinear sigma-model, Introduction to cellular and population-level systems biology with quantum gauge theory, quantum Hall theory, mean-eld theory an emphasis on synthetic biology, modeling of genetic networks, of spin liquids and quantum order, string-net condensation and cell-cell interactions, and evolutionary dynamics. Cellular systems emergence of light and fermions. include genetic switches and oscillators, network motifs, genetic X-G. Wen network evolution, and cellular decision-making. Population- level systems include models of pattern formation, cell-cell 8.514 Strongly Correlated Systems in Condensed Matter Physics communication, and evolutionary systems biology. Students taking Prereq: 8.322 and 8.333 graduate version explore the subject in more depth. Acad Year 2021-2022: Not oered J. Gore Acad Year 2022-2023: G (Spring) 3-0-9 units
Study of condensed matter systems where interactions between electrons play an important role. Topics vary depending on lecturer but may include low-dimension magnetic and electronic systems, disorder and quantum transport, magnetic impurities (the Kondo problem), quantum spin systems, the Hubbard model and high- temperature superconductors. Topics are chosen to illustrate the application of diagrammatic techniques, eld-theory approaches, and renormalization group methods in condensed matter physics. S. Todadri
Department of Physics | 15 DEPARTMENT OF PHYSICS
8.592[J] Statistical Physics in Biology 8.614[J] Introduction to Plasma Physics II Same subject as HST.452[J] Same subject as 22.612[J] Prereq: 8.333 or permission of instructor Prereq: 22.611[J] Acad Year 2021-2022: G (Spring) Acad Year 2021-2022: Not oered Acad Year 2022-2023: Not oered Acad Year 2022-2023: G (Spring) 3-0-9 units 3-0-9 units
A survey of problems at the interface of statistical physics and See description under subject 22.612[J]. modern biology: bioinformatic methods for extracting information N. Loureiro content of DNA; gene nding, sequence comparison, phylogenetic trees. Physical interactions responsible for structure of biopolymers; 8.624 Plasma Waves DNA double helix, secondary structure of RNA, elements of protein Prereq: 22.611[J] folding. Considerations of force, motion, and packaging; protein Acad Year 2021-2022: G (Spring) motors, membranes. Collective behavior of biological elements; Acad Year 2022-2023: Not oered cellular networks, neural networks, and evolution. 3-0-9 units M. Kardar, L. Mirny Comprehensive theory of electromagnetic waves in a magnetized 8.593[J] Biological Physics plasma. Wave propagation in cold and hot plasmas. Energy flow. Same subject as HST.450[J] Absorption by Landau and cyclotron damping and by transit time Prereq: 8.044 recommended but not necessary magnetic pumping (TTMP). Wave propagation in inhomogeneous G (Spring) plasma: accessibility, WKB theory, mode conversion, connection Not oered regularly; consult department formulae, and Budden tunneling. Applications to RF plasma heating, 4-0-8 units wave propagation in the ionosphere and laser-plasma interactions. Wave propagation in toroidal plasmas, and applications to ion Designed to provide seniors and rst-year graduate students with cyclotron (ICRF), electron cyclotron (ECRH), and lower hybrid (LHH) a quantitative, analytical understanding of selected biological wave heating. Quasi-linear theory and applications to RF current phenomena. Topics include experimental and theoretical basis drive in tokamaks. Extensive discussion of relevant experimental for the phase boundaries and equation of state of concentrated observations. protein solutions, with application to diseases such as sickle M. Porkolab cell anemia and cataract. Protein-ligand binding and linkage and the theory of allosteric regulation of protein function, with 8.641 Physics of High-Energy Plasmas I application to proteins as stores as transporters in respiration, Prereq: 22.611[J] enzymes in metabolic pathways, membrane receptors, regulators G (Fall) of gene expression, and self-assembling scaolds. The physics of Not oered regularly; consult department locomotion and chemoreception in bacteria and the biophysics of 3-0-9 units vision, including the theory of transparency of the eye, molecular basis of photo reception, and the detection of light as a signal-to- Physics of High-Energy Plasmas I and II address basic concepts of noise discrimination. plasmas, with temperatures of thermonuclear interest, relevant G. Benedek to fusion research and astrophysics. Microscopic transport processes due to interparticle collisions and collective modes (e.g., 8.613[J] Introduction to Plasma Physics I microinstabilities). Relevant macroscopic transport coecients Same subject as 22.611[J] (electrical resistivity, thermal conductivities, particle "diusion"). Prereq: (6.013 or 8.07) and (18.04 or Coreq: 18.075) Runaway and slide-away regimes. Magnetic reconnection G (Fall) processes and their relevance to experimental observations. 3-0-9 units Radiation emission from inhomogeneous plasmas. Conditions for thermonuclear burning and ignition (D-T and "advanced" fusion See description under subject 22.611[J]. reactions, plasmas with polarized nuclei). Role of "impurity" nuclei. N. Loureiro, I. Hutchinson "Finite-β" (pressure) regimes and ballooning modes. Convective modes in conguration and velocity space. Trapped particle regimes. Nonlinear and explosive instabilities. Interaction of positive and negative energy modes. Each subject can be taken independently. Sta
16 | Department of Physics DEPARTMENT OF PHYSICS
8.642 Physics of High-Energy Plasmas II Nuclear and Particle Physics Prereq: 22.611[J] G (Fall) 8.701 Introduction to Nuclear and Particle Physics Not oered regularly; consult department Prereq: None. Coreq: 8.321 3-0-9 units G (Fall) 3-0-9 units Physics of High-Energy Plasmas I and II address basic concepts of plasmas, with temperatures of thermonuclear interest, relevant The phenomenology and experimental foundations of particle and to fusion research and astrophysics. Microscopic transport nuclear physics; the fundamental forces and particles, composites. processes due to interparticle collisions and collective modes (e.g., Interactions of particles with matter, and detectors. SU(2), SU(3), microinstabilities). Relevant macroscopic transport coecients models of mesons and baryons. QED, weak interactions, parity (electrical resistivity, thermal conductivities, particle "diusion"). violation, lepton-nucleon scattering, and structure functions. QCD, Runaway and slide-away regimes. Magnetic reconnection gluon eld and color. W and Z elds, electro-weak unication, processes and their relevance to experimental observations. the CKM matrix. Nucleon-nucleon interactions, properties of Radiation emission from inhomogeneous plasmas. Conditions for nuclei, single- and collective- particle models. Electron and hadron thermonuclear burning and ignition (D-T and "advanced" fusion interactions with nuclei. Relativistic heavy ion collisions, and reactions, plasmas with polarized nuclei). Role of "impurity" nuclei. transition to quark-gluon plasma. "Finite-β" (pressure) regimes and ballooning modes. Convective M. Williams modes in conguration and velocity space. Trapped particle regimes. Nonlinear and explosive instabilities. Interaction of positive and 8.711 Nuclear Physics negative energy modes. Each subject can be taken independently. Prereq: 8.321 and 8.701 Sta G (Spring) 4-0-8 units 8.670[J] Principles of Plasma Diagnostics Same subject as 22.67[J] Modern, advanced study in the experimental foundations and Prereq: 22.611[J] theoretical understanding of the structure of nuclei, beginning with G (Fall) the two- and three-nucleon problems. Basic nuclear properties, 4-4-4 units collective and single-particle motion, giant resonances, mean eld models, interacting boson model. Nuclei far from stability, See description under subject 22.67[J]. nuclear astrophysics, big-bang and stellar nucleosynthesis. Electron J. Hare, A. White scattering: nucleon momentum distributions, scaling, olarization observables. Parity-violating electron scattering. Neutrino physics. 8.681, 8.682 Selected Topics in Fluid and Plasma Physics Current results in relativistic heavy ion physics and hadronic physics. Prereq: 22.611[J] Frontiers and future facilities. G (Fall, Spring) O. Hen Not oered regularly; consult department 3-0-9 units 8.712 Advanced Topics in Nuclear Physics Can be repeated for credit. Prereq: 8.711 or permission of instructor G (Fall, Spring) Presentation of topics of current interest, with content varying from Not oered regularly; consult department year to year. Subject not routinely oered; given when interest is 3-0-9 units indicated. Can be repeated for credit. Consult M. Porkolab Subject for experimentalists and theorists with rotation of the following topics: (1) Nuclear chromodynamics-- introduction to QCD, structure of nucleons, lattice QCD, phases of hadronic matter; and relativistic heavy ion collisions. (2) Medium-energy physics-- nuclear and nucleon structure and dynamics studied with medium- and high- energy probes (neutrinos, photons, electrons, nucleons, pions, and kaons). Studies of weak and strong interactions. Sta
Department of Physics | 17 DEPARTMENT OF PHYSICS
8.751[J] Quantum Technology and Devices 8.821 String Theory Same subject as 22.51[J] Prereq: 8.324 Subject meets with 22.022 Acad Year 2021-2022: Not oered Prereq: 22.11 Acad Year 2022-2023: G (Fall) G (Spring) 3-0-9 units 3-0-9 units Credit cannot also be received for 8.251
See description under subject 22.51[J]. An introduction to string theory. Basics of conformal eld theory; P. Cappellaro light-cone and covariant quantization of the relativistic bosonic string; quantization and spectrum of supersymmetric 10-dimensional 8.781, 8.782 Selected Topics in Nuclear Theory string theories; T-duality and D-branes; toroidal compactication Prereq: 8.323 and orbifolds; 11-dimensional supergravity and M-theory. Meets with G (Fall, Spring) 8.251 when oered concurrently. Not oered regularly; consult department H. Liu 3-0-9 units 8.831 Supersymmetric Quantum Field Theories Presents topics of current interest in nuclear structure and reaction Prereq: Permission of instructor theory, with content varying from year to year. Subject not routinely Acad Year 2021-2022: Not oered oered; given when sucient interest is indicated. Acad Year 2022-2023: G (Fall) Consult E. Farhi 3-0-9 units Can be repeated for credit. 8.811 Particle Physics Prereq: 8.701 Topics selected from the following: SUSY algebras and their particle G (Fall) representations; Weyl and Majorana spinors; Lagrangians of basic 3-0-9 units four-dimensional SUSY theories, both rigid SUSY and supergravity; supermultiplets of elds and superspace methods; renormalization Modern review of particles, interactions, and recent experiments. properties, and the non-renormalization theorem; spontaneous Experimental and analytical methods. QED, electroweak theory, breakdown of SUSY; and phenomenological SUSY theories. Some and the Standard Model as tested in recent key experiments at ee prior knowledge of Noether's theorem, derivation and use of and pp colliders. Mass generation, W, Z, and Higgs physics. Weak Feynman rules, l-loop renormalization, and gauge theories is decays of mesons, including heavy flavors with QCD corrections. essential. Mixing phenomena for K, D, B mesons and neutrinos. CP violation J. Thaler with results from B-factories. Future physics expectations: Higgs, SUSY, sub-structure as addressed by new experiments at the LHC 8.851 Eective Field Theory collider. Prereq: 8.324 L. Winslow Acad Year 2021-2022: G (Spring) Acad Year 2022-2023: Not oered 8.812 Graduate Experimental Physics 3-0-9 units Prereq: 8.701 Credit cannot also be received for 8.S851 G (IAP) Not oered regularly; consult department Covers the framework and tools of eective eld theory, including: 1-8-3 units identifying degrees of freedom and symmetries; power counting expansions (dimensional and otherwise); eld redenitions, bottom- Provides practical experience in particle detection with verication up and top-down eective theories; ne-tuned eective theories; by (Feynman) calculations. Students perform three experiments; matching and Wilson coecients; reparameterization invariance; at least one requires actual construction following design. Topics and advanced renormalization group techniques. Main examples are include Compton eect, Fermi constant in muon decay, particle taken from particle and nuclear physics, including the So-Collinear identication by time-of-flight, Cerenkov light, calorimeter response, Eective Theory. tunnel eect in radioactive decays, angular distribution of cosmic I. Stewart rays, scattering, gamma-gamma nuclear correlations, and modern particle localization. U. Becker
18 | Department of Physics DEPARTMENT OF PHYSICS
8.861 Advanced Topics in Superfluidity Space Physics and Astrophysics Prereq: 8.324 G (Fall) 8.901 Astrophysics I Not oered regularly; consult department Prereq: Permission of instructor 3-0-9 units G (Spring) 3-0-9 units Basic pairing theory, eective eld theory and spontaneous symmetry breaking; well-established applications to liquid helium Size and time scales. Historical astronomy. Astronomical 3 as a warm-up; research will be explored including anisotropic instrumentation. Stars: spectra and classication. Stellar structure superconductivity in heavy fermion systems and cuprates; color equations and survey of stellar evolution. Stellar oscillations. superconductivity in high-density QCD; and pairing in fermion Degenerate and collapsed stars; radio pulsars. Interacting systems with mismatched Fermi surfaces, including ultracold binary systems; accretion disks, x-ray sources. Gravitational atom systems. Additional ideas needed to discuss the fractional lenses; dark matter. Interstellar medium: HII regions, supernova quantum Hall eect will be reviewed, emphasizing its connection to remnants, molecular clouds, dust; radiative transfer; Jeans' mass; conventional superfluidity, and pointing toward aspects of anyon star formation. High-energy astrophysics: Compton scattering, behavior potentially relevant for quantum information processing. bremsstrahlung, synchrotron radiation, cosmic rays. Galactic stellar Sta distributions and populations; Oort constants; Oort limit; and globular clusters. 8.871 Selected Topics in Theoretical Particle Physics S. Hughes Prereq: 8.323 Acad Year 2021-2022: Not oered 8.902 Astrophysics II Acad Year 2022-2023: G (Fall) Prereq: 8.901 3-0-9 units G (Fall) Can be repeated for credit. 3-0-9 units
Presents topics of current interest in theoretical particle physics, Galactic dynamics: potential theory, orbits, collisionless Boltzmann with content varying from year to year. Subject not routinely oered; equation, etc. Galaxy interactions. Groups and clusters; dark given when sucient interest is indicated. matter. Intergalactic medium; x-ray clusters. Active galactic nuclei: F. Wilczek unied models, black hole accretion, radio and optical jets, etc. Homogeneity and isotropy, redshi, galaxy distance ladder. 8.872 Selected Topics in Theoretical Particle Physics Newtonian cosmology. Roberston-Walker models and cosmography. Prereq: 8.323 Early universe, primordial nucleosynthesis, recombination. Cosmic Acad Year 2021-2022: Not oered microwave background radiation. Large-scale structure, galaxy Acad Year 2022-2023: G (Fall, Spring) formation. 3-0-9 units M. McDonald Can be repeated for credit.
Presents topics of current interest in theoretical particle physics, with content varying from year to year. Subject not routinely oered; given when sucient interest is indicated. W. Taylor
8.881, 8.882 Selected Topics in Experimental Particle Physics Prereq: 8.811 G (Fall, Spring) Not oered regularly; consult department 3-0-9 units Can be repeated for credit.
Presents topics of current interest in experimental particle physics, with content varying from year to year. Subject not routinely oered; given when sucient interest is indicated. Sta
Department of Physics | 19 DEPARTMENT OF PHYSICS
8.913 Plasma Astrophysics I 8.921 Stellar Structure and Evolution Prereq: Permission of instructor Prereq: Permission of instructor G (Fall) G (Spring) Not oered regularly; consult department Not oered regularly; consult department 3-0-9 units 3-0-9 units
For students interested in space physics, astrophysics, and plasma Observable stellar characteristics; overview of observational physics in general. Magnetospheres of rotating magnetized information. Principles underlying calculations of stellar structure. planets, ordinary stars, neutron stars, and black holes. Pulsar Physical processes in stellar interiors; properties of matter and models: processes for slowing down, particle acceleration, and radiation; radiative, conductive, and convective heat transport; radiation emission; accreting plasmas and x-ray stars; stellar winds; nuclear energy generation; nucleosynthesis; and neutrino emission. heliosphere and solar wind- relevant magnetic eld conguration, Protostars; the main sequence, and the solar neutrino flux; advanced measured particle distribution in velocity space and induced evolutionary stages; variable stars; planetary nebulae, supernovae, collective modes; stability of the current sheet and collisionless white dwarfs, and neutron stars; close binary systems; and processes for magnetic reconnection; theory of collisionless shocks; abundance of chemical elements. solitons; Ferroaro-Rosenbluth sheet; solar flare models; heating Sta processes of the solar corona; Earth's magnetosphere (auroral phenomena and their interpretation, bowshock, magnetotail, 8.942 Cosmology trapped particle eects); relationship between gravitational Prereq: Permission of instructor (galactic) plasmas and electromagnetic plasmas. 8.913 deals with Acad Year 2021-2022: Not oered heliospheric, 8.914 with extra-heliospheric plasmas. Acad Year 2022-2023: G (Fall) Sta 3-0-9 units
8.914 Plasma Astrophysics II Thermal backgrounds in space. Cosmological principle and its Prereq: Permission of instructor consequences: Newtonian cosmology and types of "universes"; G (Spring) survey of relativistic cosmology; horizons. Overview of evolution in Not oered regularly; consult department cosmology; radiation and element synthesis; physical models of 3-0-9 units the "early stages." Formation of large-scale structure to variability of physical laws. First and last states. Some knowledge of relativity For students interested in space physics, astrophysics, and plasma expected. 8.962 recommended though not required. physics in general. Magnetospheres of rotating magnetized K. Masui planets, ordinary stars, neutron stars, and black holes. Pulsar models: processes for slowing down, particle acceleration, and 8.952 Particle Physics of the Early Universe radiation emission; accreting plasmas and x-ray stars; stellar winds; Prereq: 8.323; Coreq: 8.324 heliosphere and solar wind- relevant magnetic eld conguration, Acad Year 2021-2022: G (Spring) measured particle distribution in velocity space and induced Acad Year 2022-2023: Not oered collective modes; stability of the current sheet and collisionless 3-0-9 units processes for magnetic reconnection; theory of collisionless shocks; solitons; Ferroaro-Rosenbluth sheet; solar flare models; heating Basics of general relativity, standard big bang cosmology, processes of the solar corona; Earth's magnetosphere (auroral thermodynamics of the early universe, cosmic background radiation, phenomena and their interpretation, bowshock, magnetotail, primordial nucleosynthesis, basics of the standard model of particle trapped particle eects); relationship between gravitational physics, electroweak and QCD phase transition, basics of group (galactic) plasmas and electromagnetic plasmas. 8.913 deals with theory, grand unied theories, baryon asymmetry, monopoles, heliospheric, 8.914 with extra-heliospheric plasmas. cosmic strings, domain walls, axions, inflationary universe, and B. Coppi structure formation. A. Guth
20 | Department of Physics DEPARTMENT OF PHYSICS
8.962 General Relativity 8.995 Practical Experience in Physics Prereq: 8.07, 18.03, and 18.06 Prereq: None G (Spring) G (Fall, IAP, Spring, Summer) 4-0-8 units Units arranged [P/D/F] Can be repeated for credit. The basic principles of Einstein's general theory of relativity, dierential geometry, experimental tests of general relativity, black For Course 8 students participating in o-campus experiences in holes, and cosmology. physics. Before registering for this subject, students must have A. Guth an internship oer from a company or organization, must identify a Physics supervisor, and must receive prior approval from the 8.971 Astrophysics Seminar Physics Department. Upon completion of the project, student must Prereq: Permission of instructor submit a letter from the company or organization describing the work G (Fall, Spring) accomplished, along with a substantive nal report from the student Not oered regularly; consult department approved by the MIT supervisor. Consult departmental academic 2-0-4 units oce. Can be repeated for credit. Consult N. Mavalvala
Advanced seminar on current topics, with a dierent focus each 8.S301 Special Subject: Physics term. Typical topics: astronomical instrumentation, numerical and Prereq: Permission of instructor statistical methods in astrophysics, gravitational lenses, neutron G (Spring) stars and pulsars. Not oered regularly; consult department Consult D. Chakrabarty Units arranged
8.972 Astrophysics Seminar Covers topics in Physics that are not oered in the regular Prereq: Permission of instructor curriculum. Limited enrollment; preference to Physics graduate G (Fall, Spring) students. Not oered regularly; consult department A. Lightman 2-0-4 units Can be repeated for credit. 8.S372 Special Subject: Physics Prereq: None Advanced seminar on current topics, with a dierent focus each term. Acad Year 2021-2022: Not oered Typical topics: gravitational lenses, active galactic nuclei, neutron Acad Year 2022-2023: G (Fall) stars and pulsars, galaxy formation, supernovae and supernova 3-0-9 units remnants, brown dwarfs, and extrasolar planetary systems. The presenter at each session is selected by drawing names from a hat Covers topics in Physics that are not oered in the regular containing those of all attendees. Oered if sucient interest is curriculum. indicated. A. Harrow Consult D. Chakrabarty 8.S396 Special Subject: Physics 8.981, 8.982 Selected Topics in Astrophysics Prereq: None Prereq: Permission of instructor G (Spring; rst half of term) G (Spring) Units arranged [P/D/F] Not oered regularly; consult department 3-0-9 units Covers topics in Physics that are not oered in the regular Can be repeated for credit. curriculum. A. Frebel Topics of current interest, varying from year to year. Subject not routinely oered; given when sucient interest is indicated. Consult D. Chakrabarty
Department of Physics | 21 DEPARTMENT OF PHYSICS
8.S397 Special Subject: Physics Prereq: None G (Spring; second half of term) Units arranged [P/D/F]
Covers topics in Physics that are not oered in the regular curriculum. A. Frebel
8.S421 Special Subject: Physics Prereq: Permission of instructor G (Fall) Not oered regularly; consult department Units arranged Can be repeated for credit.
Opportunity for group study of subjects in physics not otherwise included in the curriculum. W. Ketterle
8.THG Graduate Physics Thesis Prereq: Permission of instructor G (Fall, IAP, Spring, Summer) Units arranged Can be repeated for credit.
Program of research leading to the writing of an SM, PhD, or ScD thesis; to be arranged by the student and an appropriate MIT faculty member. Consult I. Stewart
22 | Department of Physics