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Quantum Field Theory in a Nutshell
A. Zee

Book Description | Reviews
Chapter 1 [in PDF format]

TABLE OF CONTENTS:

Preface xi
Convention, Notation, and Units xv
PART I: MOTIVATION AND FOUNDATION
I.1 Who Needs It? 3
I.2 Path Integral Formulation of Quantum Physics 7
I.3 From Mattress to Field 16
I.4 From Field to Particle to Force 24
I.5 Coulomb and Newton: Repulsion and Attraction 30
I.6 Inverse Square Law and the Floating 3-Brane 38
I.7 Feynman Diagrams 41
I.8 Quantizing Canonically and Disturbing the Vacuum 61
I.9 Symmetry 70
I.10 Field Theory in Curved Spacetime 76
I.11 Field Theory Redux 84
PART II: DIRAC AND THE SPINOR
II.1 The Dirac Equation 89
II.2 Quantizing the Dirac Field 103
II.3 Lorentz Group and Weyl Spinors 111
II.4 Spin-Statistics Connection 117
II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagrams for Fermions 121
II.6 Electron Scattering and Gauge Invariance 130
II.7 Diagrammatic Proof of Gauge Invariance 135
PART III: RENORMALIZATION AND GAUGE INVARIANCE
III.1 Cutting Off Our Ignorance 145
III.2 Renormalizable versus Nonrenormalizable 154
III.3 Counterterms and Physical Perturbation Theory 158
III.4 Gauge Invariance: A Photon Can Find No Rest 167
III.5 Field Theory without Relativity 172
III.6 The Magnetic Moment of the Electron 177
III.7 Polarizing the Vacuum and Renormalizing the Charge 183
PART IV: SYMMETRY AND SYMMETRY BREAKING
IV.1 Symmetry Breaking 193
IV.2 The Pion as a Nambu-Goldstone Boson 202
IV.3 Effective Potential 208
IV.4 Magnetic Monopole 217
IV.5 Nonabelian Gauge Theory 226
IV.6 The Anderson-Higgs Mechanism 236
IV.7 Chiral Anomaly 243
PART V: FIELD THEORY AND COLLECTIVE PHENOMENA
V.1 Superfluids 257
V.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature 261
V.3 Landau-Ginzburg Theory of Critical Phenomena 267
V.4 Superconductivity 270
V.5 Peierls Instability 273
V.6 Solitons 277
V.7 Vortices, Monopoles, and Instantons 282
PART VI: FIELD THEORY AND CONDENSED MATTER
VI.1 Fractional Statistics, Chern-Simons Term, and Topological
Field Theory 293
VI.2 Quantum Hall Fluids 300
VI.3 Duality 309
VI.4 The s Models as Effective Field Theories 318
VI.5 Ferromagnets and Antiferromagnets 322
VI.6 Surface Growth and Field Theory 326
VI.7 Disorder: Replicas and Grassmannian Symmetry 330
VI.8 Renormalization Group Flow as a Natural Concept in
High Energy and Condensed Matter Physics 337
PART VII: GRAND UNIFICATION
VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory 353
VII.2 Electroweak Unification 361
VII.3 Quantum Chromodynamics 368
VII.4 Large N Expansion 377
VII.5 Grand Unification 391
VII.6 Protons Are Not Forever 397
VII.7 SO(10) Unification 405
PART VIII: GRAVITY AND BEYOND
VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture 419
VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problem 434
VIII.3 Effective Field Theory Approach to Understanding Nature.437
VIII.4 Supersymmetry: A Very Brief Introduction 443
VIII.5 A Glimpse of String Theory as a 2-Dimensional Field Theory 452
Closing Words 455
APPENDIXES:
A. Gaussian Integration and the Central Identity of Quantum Field Theory 459
B. A Brief Review of Group Theory 461
C. Feynman Rules 471
D. Various Identities and Feynman Integrals 475
E. Dotted and Undotted Indices and the Majorana Spinor 479
Solutions to Selected Exercises 483
Further Reading 501
Index 505
Closing Words 455
APPENDIXES:
A. Gaussian Integration and the Central Identity of Quantum Field Theory 459
B. A Brief Review of Group Theory 461
C. Feynman Rules 471
D. Various Identities and Feynman Integrals 475
E. Dotted and Undotted Indices and the Majorana Spinor 479
Solutions to Selected Exercises 483
Further Reading 501
Index 505

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File created: 4/17/2014

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