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A. Zee

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"A beautiful exposition of the way modern field theorists think about quantum field theory, packed with insights and physical intuition. Zee's book should be required reading for every serious student of the subject."--Nima Arkani-Hamed, Institute for Advanced Study

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Quantum Field Theory in a Nutshell

PRINCETON UNIVERSITY PRESS

Contents

Preface to the First Edition...........................................................................................xvPreface to the Second Edition..........................................................................................xixConvention, Notation, and Units........................................................................................xxvI.1 Who Needs It?...................................................................................................3I.2 Path Integral Formulation of Quantum Physics....................................................................7I.3 From Mattress to Field..........................................................................................17I.4 From Field to Particle to Force.................................................................................26I.5 Coulomb and Newton: Repulsion and Attraction....................................................................32I.6 Inverse Square Law and the Floating 3-Brane.....................................................................40I.7 Feynman Diagrams................................................................................................43I.8 Quantizing Canonically..........................................................................................61I.9 Disturbing the Vacuum...........................................................................................70I.10 Symmetry........................................................................................................76I.11 Field Theory in Curved Spacetime................................................................................81I.12 Field Theory Redux..............................................................................................88II.1 The Dirac Equation..............................................................................................93II.2 Quantizing the Dirac Field......................................................................................107II.3 Lorentz Group and Weyl Spinors..................................................................................114II.4 Spin-Statistics Connection......................................................................................120II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions...........................................123II.6 Electron Scattering and Gauge Invariance........................................................................132II.7 Diagrammatic Proof of Gauge Invariance..........................................................................144II.8 Photon-Electron Scattering and Crossing.........................................................................152III.1 Cutting Off Our Ignorance.......................................................................................161III.2 Renormalizable versus Nonrenormalizable.........................................................................169III.3 Counterterms and Physical Perturbation Theory...................................................................173III.4 Gauge Invariance: A Photon Can Find No Rest.....................................................................182III.5 Field Theory without Relativity.................................................................................190III.6 The Magnetic Moment of the Electron.............................................................................194III.7 Polarizing the Vacuum and Renormalizing the Charge..............................................................200III.8 Becoming Imaginary and Conserving Probability...................................................................207IV.1 Symmetry Breaking...............................................................................................223IV.2 The Pion as a Nambu-Goldstone Boson.............................................................................231IV.3 Effective Potential.............................................................................................237IV.4 Magnetic Monopole...............................................................................................245IV.5 Nonabelian Gauge Theory.........................................................................................253IV.6 The Anderson-Higgs Mechanism....................................................................................263IV.7 Chiral Anomaly..................................................................................................270V.1 Superfluids.....................................................................................................283V.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature..............................................287V.3 Landau-Ginzburg Theory of Critical Phenomena....................................................................292V.4 Superconductivity...............................................................................................295V.5 Peierls Instability.............................................................................................298V.6 Solitons........................................................................................................302V.7 Vortices, Monopoles, and Instantons.............................................................................306VI.1 Fractional Statistics, Chern-Simons Term, and Topological Field Theory..........................................315VI.2 Quantum Hall Fluids.............................................................................................322VI.3 Duality.........................................................................................................331VI.4 The s Models as Effective Field Theories........................................................................340VI.5 Ferromagnets and Antiferromagnets...............................................................................344VI.6 Surface Growth and Field Theory.................................................................................347VI.7 Disorder: Replicas and Grassmannian Symmetry....................................................................350VI.8 Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics.....................356VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory...........................................................371VII.2 Electroweak Unification.........................................................................................379VII.3 Quantum Chromodynamics..........................................................................................385VII.4 Large N Expansion...............................................................................................394VII.5 Grand Unification...............................................................................................407VII.6 Protons Are Not Forever.........................................................................................413VII.7 SO(10) Unification..............................................................................................421VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture..........................................................433VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problems...........................................448VIII.3 Effective...