Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
An Introduction to Quantum Field Theory
AN INTRODUCTION TO QUANTUM FIELD THEORY By Dr M Dasgupta University of Manchester Lecture presented at the School for Experimental High Energy Physics Students Somerville College, Oxford, September 2009 - 1 - - 2 - Contents 0 Prologue....................................................................................................... 5 1 Introduction ................................................................................................ 6 1.1 Lagrangian formalism in classical mechanics......................................... 6 1.2 Quantum mechanics................................................................................... 8 1.3 The Schrödinger picture........................................................................... 10 1.4 The Heisenberg picture............................................................................ 11 1.5 The quantum mechanical harmonic oscillator ..................................... 12 Problems .............................................................................................................. 13 2 Classical Field Theory............................................................................. 14 2.1 From N-point mechanics to field theory ............................................... 14 2.2 Relativistic field theory ............................................................................ 15 2.3 Action for a scalar field ............................................................................ 15 2.4 Plane wave solution to the Klein-Gordon equation ........................... -
Macroscopic Quantum Phenomena in Interacting Bosonic Systems: Josephson flow in Liquid 4He and Multimode Schr¨Odingercat States
Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states by Tyler James Volkoff A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemistry in the Graduate Division of the University of California, Berkeley Committee in charge: Professor K. Birgitta Whaley, Chair Professor Philip L. Geissler Professor Richard E. Packard Fall 2014 Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states Copyright 2014 by Tyler James Volkoff 1 Abstract Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states by Tyler James Volkoff Doctor of Philosophy in Chemistry University of California, Berkeley Professor K. Birgitta Whaley, Chair In this dissertation, I analyze certain problems in the following areas: 1) quantum dynam- ical phenomena in macroscopic systems of interacting, degenerate bosons (Parts II, III, and V), and 2) measures of macroscopicity for a large class of two-branch superposition states in separable Hilbert space (Part IV). Part I serves as an introduction to important concepts recurring in the later Parts. In Part II, a microscopic derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3 + 1)D microscopic model with local U(1) gauge symmetry is presented. The effec- tive theory is applied to the transition from linear to sinusoidal current vs. phase behavior observed in recent experiments on liquid 4He driven through nanoaperture arrays. Part III discusses path-integral Monte Carlo (PIMC) numerical simulations of quantum hydrody- namic properties of reservoirs of He II communicating through simple nanoaperture arrays. -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
The Mechanics of the Fermionic and Bosonic Fields: an Introduction to the Standard Model and Particle Physics
The Mechanics of the Fermionic and Bosonic Fields: An Introduction to the Standard Model and Particle Physics Evan McCarthy Phys. 460: Seminar in Physics, Spring 2014 Aug. 27,! 2014 1.Introduction 2.The Standard Model of Particle Physics 2.1.The Standard Model Lagrangian 2.2.Gauge Invariance 3.Mechanics of the Fermionic Field 3.1.Fermi-Dirac Statistics 3.2.Fermion Spinor Field 4.Mechanics of the Bosonic Field 4.1.Spin-Statistics Theorem 4.2.Bose Einstein Statistics !5.Conclusion ! 1. Introduction While Quantum Field Theory (QFT) is a remarkably successful tool of quantum particle physics, it is not used as a strictly predictive model. Rather, it is used as a framework within which predictive models - such as the Standard Model of particle physics (SM) - may operate. The overarching success of QFT lends it the ability to mathematically unify three of the four forces of nature, namely, the strong and weak nuclear forces, and electromagnetism. Recently substantiated further by the prediction and discovery of the Higgs boson, the SM has proven to be an extraordinarily proficient predictive model for all the subatomic particles and forces. The question remains, what is to be done with gravity - the fourth force of nature? Within the framework of QFT theoreticians have predicted the existence of yet another boson called the graviton. For this reason QFT has a very attractive allure, despite its limitations. According to !1 QFT the gravitational force is attributed to the interaction between two gravitons, however when applying the equations of General Relativity (GR) the force between two gravitons becomes infinite! Results like this are nonsensical and must be resolved for the theory to stand. -
Feynman Diagrams, Momentum Space Feynman Rules, Disconnected Diagrams, Higher Correlation Functions
PHY646 - Quantum Field Theory and the Standard Model Even Term 2020 Dr. Anosh Joseph, IISER Mohali LECTURE 05 Tuesday, January 14, 2020 Topics: Feynman Diagrams, Momentum Space Feynman Rules, Disconnected Diagrams, Higher Correlation Functions. Feynman Diagrams We can use the Wick’s theorem to express the n-point function h0jT fφ(x1)φ(x2) ··· φ(xn)gj0i as a sum of products of Feynman propagators. We will be interested in developing a diagrammatic interpretation of such expressions. Let us look at the expression containing four fields. We have h0jT fφ1φ2φ3φ4g j0i = DF (x1 − x2)DF (x3 − x4) +DF (x1 − x3)DF (x2 − x4) +DF (x1 − x4)DF (x2 − x3): (1) We can interpret Eq. (1) as the sum of three diagrams, if we represent each of the points, x1 through x4 by a dot, and each factor DF (x − y) by a line joining x to y. These diagrams are called Feynman diagrams. In Fig. 1 we provide the diagrammatic interpretation of Eq. (1). The interpretation of the diagrams is the following: particles are created at two spacetime points, each propagates to one of the other points, and then they are annihilated. This process can happen in three different ways, and they correspond to the three ways to connect the points in pairs, as shown in the three diagrams in Fig. 1. Thus the total amplitude for the process is the sum of these three diagrams. PHY646 - Quantum Field Theory and the Standard Model Even Term 2020 ⟨0|T {ϕ1ϕ2ϕ3ϕ4}|0⟩ = DF(x1 − x2)DF(x3 − x4) + DF(x1 − x3)DF(x2 − x4) +DF(x1 − x4)DF(x2 − x3) 1 2 1 2 1 2 + + 3 4 3 4 3 4 Figure 1: Diagrammatic interpretation of Eq. -
An Introduction to Supersymmetry
An Introduction to Supersymmetry Ulrich Theis Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D–07743 Jena, Germany [email protected] This is a write-up of a series of five introductory lectures on global supersymmetry in four dimensions given at the 13th “Saalburg” Summer School 2007 in Wolfersdorf, Germany. Contents 1 Why supersymmetry? 1 2 Weyl spinors in D=4 4 3 The supersymmetry algebra 6 4 Supersymmetry multiplets 6 5 Superspace and superfields 9 6 Superspace integration 11 7 Chiral superfields 13 8 Supersymmetric gauge theories 17 9 Supersymmetry breaking 22 10 Perturbative non-renormalization theorems 26 A Sigma matrices 29 1 Why supersymmetry? When the Large Hadron Collider at CERN takes up operations soon, its main objective, besides confirming the existence of the Higgs boson, will be to discover new physics beyond the standard model of the strong and electroweak interactions. It is widely believed that what will be found is a (at energies accessible to the LHC softly broken) supersymmetric extension of the standard model. What makes supersymmetry such an attractive feature that the majority of the theoretical physics community is convinced of its existence? 1 First of all, under plausible assumptions on the properties of relativistic quantum field theories, supersymmetry is the unique extension of the algebra of Poincar´eand internal symmtries of the S-matrix. If new physics is based on such an extension, it must be supersymmetric. Furthermore, the quantum properties of supersymmetric theories are much better under control than in non-supersymmetric ones, thanks to powerful non- renormalization theorems. -
Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
PHYSICAL REVIEW X 3, 011016 (2013) Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect Ashvin Vishwanath Department of Physics, University of California, Berkeley, California 94720, USA Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA T. Senthil Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 4 October 2012; revised manuscript received 31 December 2012; published 28 February 2013) We discuss physical properties of ‘‘integer’’ topological phases of bosons in D ¼ 3 þ 1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free- fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response , which, somewhat surprisingly, is an odd multiple of 2.Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term. -
Clifford Algebras, Multipartite Systems and Gauge Theory Gravity
Mathematical Phyiscs Clifford Algebras, Multipartite Systems and Gauge Theory Gravity Marco A. S. Trindadea Eric Pintob Sergio Floquetc aColegiado de Física Departamento de Ciências Exatas e da Terra Universidade do Estado da Bahia, Salvador, BA, Brazil bInstituto de Física Universidade Federal da Bahia Salvador, BA, Brazil cColegiado de Engenharia Civil Universidade Federal do Vale do São Francisco Juazeiro, BA, Brazil. E-mail: [email protected], [email protected], [email protected] Abstract: In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space-time algebra for gravitation developed by Lasenby and Do- ran (Lasenby, A. N., Doran, C. J. L, and Gull, S.F.: Gravity, gauge theories and geometric algebra. Phil. Trans. R. Soc. Lond. A, 582, 356:487 (1998)). We associate the gauge fields with description of fermionic and bosonic states using the generalized graded tensor product. Einstein’s equations are deduced from the graded projections and an algebraic Hopf-like structure naturally emerges from formalism. A connection with the theory of the quantum information is performed through the minimal left ideals and entangled qubits are derived. In addition applications to black holes physics and standard model are outlined. arXiv:1807.09587v2 [physics.gen-ph] 16 Nov 2018 1Corresponding author. Contents 1 Introduction1 2 General formulation and Einstein field equations3 3 Qubits 9 4 Black holes background 10 5 Standard model 11 6 Conclusions 15 7 Acknowledgements 16 1 Introduction This work is dedicated to the memory of professor Waldyr Alves Rodrigues Jr., whose contributions in the field of mathematical physics were of great prominence, especially in the study of clifford algebras and their applications to physics [1]. -
Arxiv:1809.08749V3 [Quant-Ph] 5 Dec 2018 a General Guiding Principle in Building the Theory of Fun- Damental Interactions (See, E.G., [1,3])
Resolution of Gauge Ambiguities in Ultrastrong-Coupling Cavity QED Omar Di Stefano,1 Alessio Settineri,2 Vincenzo Macr`ı,1 Luigi Garziano,1 Roberto Stassi,1 Salvatore Savasta,1, 2, ∗ and Franco Nori1, 3 1Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan 2Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Universit`adi Messina, I-98166 Messina, Italy 3Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA Gauge invariance is the cornerstone of modern quantum field theory [1{4]. Recently, it has been shown that the quantum Rabi model, describing the dipolar coupling between a two-level atom and a quantized electromagnetic field, violates this principle [5{7]. This widely used model describes a plethora of quantum systems and physical processes under different interaction regimes [8,9]. In the ultrastrong coupling regime, it provides predictions which drastically depend on the chosen gauge. This failure is attributed to the finite-level truncation of the matter system. We show that a careful application of the gauge principle is able to restore gauge invariance even for extreme light- matter interaction regimes. The resulting quantum Rabi Hamiltonian in the Coulomb gauge differs significantly from the standard model and provides the same physical results obtained by using the dipole gauge. It contains field operators to all orders that cannot be neglected when the coupling strength is high. These results shed light on subtleties of gauge invariance in the nonperturbative and extreme interaction regimes, which are now experimentally accessible, and solve all the long-lasting controversies arising from gauge ambiguities in the quantum Rabi and Dicke models [5, 10{18]. -
Keference International Centre for Theoretical
KEFERENCE INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS IC/86/342 INTERNATIONAL THE REGULAR EFFECTIVE ACTION OF GAUGE FIELD THEORY AND QUANTUM GRAVITY ATOMIC ENERGY AGENCY Nazir S. Baaklini UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION IC/86/342 International Atomic Energy Agency 0. INTRODUCTION and The effective action of quantum field theory, defined by the functional United Nations Educational Scientific and Cultural Organization integral , is an elegant and potentially, very powerful framework for compu- INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ting quantum effects, in a manner that preserves underlying fundamental symmetries. However, this framework had been utilized mainly in computing effective potentials, and in certain discussions of the divergent counter-terms needed in gauge field THE REGULAR EFFECTIVE ACTION OF GAUGE FIELD THEORY theory and quantum gravity. Whereas it should ~ae very fruitful fo develop expre- AND QUANTUM GRAVITY ssions for the effective action which could have general applicability, computa- tions are still performed using conventional Feynman rules. What is needed is a perturbative formalism for the effective action vhicii applies to a general field Nazir S. Baaklini theory containing Bosonic as well as Fermionic fields, and vhich could be used to International Centre for Theoretical Physics, Trieste, Italy address fundamental issues of quantum field theory and quantum gravity. and Dahr el Chir Science Centre, Dhour el Choueir, Lebanon. On the other hand, our study of the effective action makes impact on two fundamental issues. One of these concerns the treatment of gauge field theory and other singular systems. The other concerns the ultraviolet divergences of quantum field theory and quantum gravity. -
Solutions 4: Free Quantum Field Theory
QFT PS4 Solutions: Free Quantum Field Theory (22/10/18) 1 Solutions 4: Free Quantum Field Theory 1. Heisenberg picture free real scalar field We have Z 3 d p 1 −i!pt+ip·x y i!pt−ip·x φ(t; x) = 3 p ape + ape (1) (2π) 2!p (i) By taking an explicit hermitian conjugation, we find our result that φy = φ. You need to note that all the parameters are real: t; x; p are obviously real by definition and if m2 is real and positive y y semi-definite then !p is real for all values of p. Also (^a ) =a ^ is needed. (ii) Since π = φ_ = @tφ classically, we try this on the operator (1) to find Z d3p r! π(t; x) = −i p a e−i!pt+ip·x − ay ei!pt−ip·x (2) (2π)3 2 p p (iii) In this question as in many others it is best to leave the expression in terms of commutators. That is exploit [A + B; C + D] = [A; C] + [A; D] + [B; C] + [B; D] (3) as much as possible. Note that here we do not have a sum over two terms A and B but a sum over an infinite number, an integral, but the principle is the same. −i!pt+ip·x −ipx The second way to simplify notation is to write e = e so that we choose p0 = +!p. −i!pt+ip·x ^y y −i!pt+ip·x The simplest way however is to write Abp =a ^pe and Ap =a ^pe . -
A Supersymmetry Primer
hep-ph/9709356 version 7, January 2016 A Supersymmetry Primer Stephen P. Martin Department of Physics, Northern Illinois University, DeKalb IL 60115 I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motiva- tions for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experi- mental signals for supersymmetry, and some extensions of the minimal framework. Contents 1 Introduction 3 2 Interlude: Notations and Conventions 13 3 Supersymmetric Lagrangians 17 3.1 The simplest supersymmetric model: a free chiral supermultiplet ............. 18 3.2 Interactions of chiral supermultiplets . ................ 22 3.3 Lagrangians for gauge supermultiplets . .............. 25 3.4 Supersymmetric gauge interactions . ............. 26 3.5 Summary: How to build a supersymmetricmodel . ............ 28 4 Superspace and superfields 30 4.1 Supercoordinates, general superfields, and superspace differentiation and integration . 31 4.2 Supersymmetry transformations the superspace way . ................ 33 4.3 Chiral covariant derivatives . ............ 35 4.4 Chiralsuperfields................................ ........ 37 arXiv:hep-ph/9709356v7 27 Jan 2016 4.5 Vectorsuperfields................................ ........ 38 4.6 How to make a Lagrangian in superspace . .......... 40 4.7 Superspace Lagrangians for chiral supermultiplets . ................... 41 4.8 Superspace Lagrangians for Abelian gauge theory . ................ 43 4.9 Superspace Lagrangians for general gauge theories . ................. 46 4.10 Non-renormalizable supersymmetric Lagrangians . .................. 49 4.11 R symmetries........................................