Physics 630 Quantum Field Theory III (3 Credits)

Physics 630

Quantum Field Theory III (3 credits) Fall 2012

Instructor: Prof. Michael Eides 279 Chem.-Phys. Bldg. Phone 257-3997 E-mail: [email protected] Office hours: Tuesday, 2:00-4:00 pm, or by appointment. Class meets Tuesday, Thursday, 9:30-10:45 am (CP 183). There will be no classes on Tuesday, Novem- ber 6 (Presidential Election Day – Academic Holiday), and Thursday, November 22 (Academic Holidays). Grading: I will give you home assignments approximately every couple of weeks. Your homework will be graded (40 points). Solutions to the problems will be placed in the library. I advice you to read my solutions with great care. If you have any questions about my solutions (as I expect you would), you are welcome in my office for discussion. I encourage you to discuss the homework together, and even to work on it together. However, you should write up your homework separately. Identical solutions would not earn any points. There will be no midterm exam. There will be a take-home final exam due Tuesday, December 11 (60 points). It could happen that I will change my mind and ask each of you to prepare a short talk (20-25 min) instead of the final exam. Student Evaluations: Course evaluations are an important (and mandatory!) component of our De- partment’s instructional program. The evaluation window for Fall 2012 will open on Wednesday, November 14, and close on Wednesday, December 5th. To access the system during this time, simply go to ”Courses” on the A&S Departmental Website page, and click on the link for Course Evaluations; then follow the instructions. You will need to use your student ID# to log into the system, and this will also allow us to monitor who has filled out evaluations. However, when you log-in you will be assigned a random number that will keep all your comments and scores anonymous.

Textbook: M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison- Wesley, 1995, ISBN 0-201-50397-2. You can ﬁnd corrections to the printed version at http://www.slac.stanford.edu/∼mpeskin/QFT.html Other useful books:

• All books that were on this list last semester.

• T. Banks, Modern Quantum Field Theory, Cambridge University Press, 2008.

• P. Ramond, Field Theory: A Modern Primer, 2nd edition, 1989.

• S. Weinberg, The Quantum Theory of Fields, volumes I, II, Cambridge University Press, 1996.

• J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 3d edition, 1996.

• P. Ramond, Journeys Beyond the Standard Model, Perseus Books, 1999.

• M. Dine, Supersymmetry and String Theory: Beyond the Standard Model, CAM, 2007.

• G. G. Ross, Grand Uniﬁed Theories, Westview, 1984.

• P. West, Introduction to Supersymmetry and Supergravity, World Scientiﬁc, 1986. • N. Polonsky, Supersymmetry: Structure and Phenomena, Springer, 2001.

• R. Rajaraman, Solitons and Instantons, Elsevier, 1987. The Syllabus

1. Functional Methods in QFT

• Equations of Motion and Schwinger-Dyson Equations. Local Conservation Laws. Ward-Takahashi Identities. • Generating Functional and Eﬀective Action in QFT. • Eﬀective Potential, Renormalization Group Improvement. • Quantum Goldstone Theorem. Coleman-Weinberg Potential and Spontaneous Symmetry Break- ing.

2. Nonabelian Gauge Theories

• Basics of Compact Internal Symmetry Groups. • Classical and Quantum Nonabelian Gauge Theories. Quantization and Faddeev-Popov Trick. • One-Loop Divergencies and Calculation of β-Function. • Background Field Method and Charge Renormalization. • Asymptotic Freedom and Infrared Slavery. Dimensional Transmutation.

3. Perturbative QCD and Operator Product Expansion. Composite Operators

• Electron-Positron Annihilation into Hadrons. Space-Time Picture. Cross Section and Polariza- tion Operator. • Operator Product Expansion at Short Distances. Operator Analysis of Annihilation. Dispersion Relations and Moments of Polarization Operator at Large Spacelike Momenta. SVZ Sum Rules. • Deep Inelastic Scattering, Kinematics, Structure Functions. Space-Time Picture. Quark Parton Model. DGLAP Equations. • Space-Time Picture of Deep Inelastic Scattering. Light Cone Operator Product Expansion. Dis- persion Integrals and Moments of Structure Functions. • Composite Operators, Renormalization Group Equations for OPE Coeﬃcients. • Anomalous Dimensions and Evolution of Moments of Structure Functions. Connection between OPE and DGLAP Analysis of Deep Inelastic Scattering.

4. Spontaneously Broken Nonabelian Gauge Theories

• Summary of Phenomenology of Weak Interactions. • Nonabelian Higgs Eﬀect. • Glashow-Weinberg-Salam Theory of Electroweak Interactions. • Limits on the Higgs Mass from Stability and Triviality of the Eﬀective Potential.

5. Anomalies • Axial Anomaly in Two-Dimensional QED. Diagrammatic Calculation, Schwinger Point Splitting Method, Functional Integral Calculation. • Axial Anomaly in Real QED. Diagrammatic Calculation, Schwinger Point Splitting Method, Functional Integral Calculation. • Axial Anomaly in Nonabelian Gauge Theories. Cancelation of Anomalies in the Standard Model. • Spontaneous Breaking of Chiral Invariance in QCD. How to Measure Number of Colors: QED Axial Anomaly and Decay π0 → 2γ. • Anomalous Breaking of Scale Invariance and Trace of the Energy-Momentum Tensor in QED and QCD.

6. Beyond the Standard Model. Grand Uniﬁed Theories

• More on the Standard Model, its Achievements and Drawbacks. • Running of the Coupling Constants and Uniﬁcation. • Construction of SU(5) GUT. • Predictions of GUTS. Proton Decay.

7. Beyond the Standard Model. Supersymmetry

• Coleman-Mandula Theorem. • Basics of SUSY: Multiplets, Lagrangians, Superspace Formalism. • The Hierarchy Problem. Minimal Supersymmetric Stadard Model. • Supersymmetric GUTS.

8. Nonperturbative Dynamics: Instantons and Solitons

• Instantons in Quantum Mechanics. Dilute Instanton Gas Approximation. • Instantons in QCD. QCD Vacuum Structure. • Solitons in Nonlinear Field Theories. Quantization of Solitons. Solitons as Nonperturbative Quantum Particles.