Quantum Field Theory in a Nutshell

✍ Scribed by Zee A.

• Publisher: PUP
• Year: 2010
• Tongue: English
• Leaves: 605
• Series: In a Nutshell
• Edition: 2ed
• Category: Library

✦ Synopsis

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.The most accessible and comprehensive introductory textbook available Features a fully revised, updated, and expanded text Covers the latest exciting advances in the field Includes new exercises Offers a one-of-a-kind resource for students and researchersLeading universities that have adopted this book include: Arizona State University Boston University Brandeis University Brown University California Institute of Technology Carnegie Mellon College of William & Mary Cornell Harvard University Massachusetts Institute of Technology Northwestern University Ohio State University Princeton University Purdue University - Main Campus Rensselaer Polytechnic Institute Rutgers University - New Brunswick Stanford University University of California - Berkeley University of Central Florida University of Chicago University of Michigan University of Montreal University of Notre Dame Vanderbilt University Virginia Tech University

✦ Table of Contents

Title......Page 8
Copyright......Page 9
Contents......Page 12
Preface to the First Edition......Page 16
Preface to the Second Edition......Page 20
Convention, Notation, and Units......Page 26
I: Part I: Motivation and Foundation......Page 30
I.1 Who Needs It?......Page 32
I.2 Path Integral Formulation of Quantum Physics......Page 36
I.3 From Mattress to Field......Page 46
I.4 From Field to Particle to Force......Page 55
I.5 Coulomb and Newton: Repulsion and Attraction......Page 61
I.6 Inverse Square Law and the Floating 3-Brane......Page 69
I.7 Feynman Diagrams......Page 72
I.8 Quantizing Canonically......Page 90
I.9 Disturbing the Vacuum......Page 99
I.10 Symmetry......Page 105
I.11 Field Theory in Curved Spacetime......Page 110
I.12 Field Theory Redux......Page 117
II: Part II: Dirac and the Spinor......Page 120
II.1 The Dirac Equation......Page 122
II.2 Quantizing the Dirac Field......Page 136
II.3 Lorentz Group and Weyl Spinors......Page 143
II.4 Spin-Statistics Connection......Page 149
II.5 Vacuum Energy, Grassmann Integrals, and Feynman Diagramsfor Fermions......Page 152
II.6 Electron Scattering and Gauge Invariance......Page 161
II.7 Diagrammatic Proof of Gauge Invariance......Page 173
II.8 Photon-Electron Scattering and Crossing......Page 181
III: Part III: Renormalization and Gauge Invariance......Page 188
III.1 Cutting Off Our Ignorance......Page 190
III.2 Renormalizable versus Nonrenormalizable......Page 198
III.3 Counterterms and Physical Perturbation Theory......Page 202
III.4 Gauge Invariance: A Photon Can Find No Rest......Page 211
III.5 Field Theory without Relativity......Page 219
III.6 The Magnetic Moment of the Electron......Page 223
III.7 Polarizing the Vacuum and Renormalizing the Charge......Page 229
III.8 Becoming Imaginary and Conserving Probability......Page 236
IV: Part IV: Symmetry and Symmetry Breaking......Page 250
IV.1 Symmetry Breaking......Page 252
IV.2 The Pion as a Nambu-Goldstone Boson......Page 260
IV.3 Effective Potential......Page 266
IV.4 Magnetic Monopole......Page 274
IV.5 Nonabelian Gauge Theory......Page 282
IV.6 The Anderson-Higgs Mechanism......Page 292
IV.7 Chiral Anomaly......Page 299
V: Part V: Field Theory and Collective Phenomena......Page 310
V.1 Superfluids......Page 312
V.2 Euclid, Boltzmann, Hawking, and Field Theory at Finite Temperature......Page 316
V.3 Landau-Ginzburg Theory of Critical Phenomena......Page 321
V.4 Superconductivity......Page 324
V.5 Peierls Instability......Page 327
V.6 Solitons......Page 331
V.7 Vortices, Monopoles, and Instantons......Page 335
VI: Part VI: Field Theory and Condensed Matter......Page 342
VI.1 Fractional Statistics, Chern-Simons Term, and Topological Field Theory......Page 344
VI.2 Quantum Hall Fluids......Page 351
VI.3 Duality......Page 360
VI.4 The σ Models as Effective Field Theories......Page 369
VI.5 Ferromagnets and Antiferromagnets......Page 373
VI.6 Surface Growth and Field Theory......Page 376
VI.7 Disorder: Replicas and Grassmannian Symmetry......Page 379
VI.8 Renormalization Group Flow as a Natural Concept in High Energy and Condensed Matter Physics......Page 385
VII: Part VII: Grand Unification......Page 398
VII.1 Quantizing Yang-Mills Theory and Lattice Gauge Theory......Page 400
VII.2 Electroweak Unification......Page 408
VII.3 Quantum Chromodynamics......Page 414
VII.4 Large N Expansion......Page 423
VII.5 Grand Unification......Page 436
VII.6 Protons Are Not Forever......Page 442
VII.7 SO(10) Unification......Page 450
VIII: Part VIII: Gravity and Beyond......Page 460
VIII.1 Gravity as a Field Theory and the Kaluza-Klein Picture......Page 462
VIII.2 The Cosmological Constant Problem and the Cosmic Coincidence Problems......Page 477
VIII.3 Effective Field Theory Approach to Understanding Nature......Page 481
VIII.4 Supersymmetry: A Very Brief Introduction......Page 490
VIII.5 A Glimpse of String Theory as a 2-Dimensional Field Theory......Page 498
Closing Words......Page 502
N: Part N......Page 506
N.1 Gravitational Waves and Effective Field Theory......Page 508
N.2 Gluon Scattering in Pure Yang-Mills Theory......Page 512
N.3 Subterranean Connections in Gauge Theories......Page 526
N.4 Is Einstein Gravity Secretly the Square of Yang-Mills Theory?......Page 542
More Closing Words......Page 550
Appendix A: Gaussian Integration and the Central Identity of Quantum Field Theory......Page 552
Appendix B: A Brief Review of Group Theory......Page 554
Appendix C: Feynman Rules......Page 563
Appendix D: Various Identities and Feynman Integrals......Page 567
Appendix E: Dotted and Undotted Indices and the Majorana Spinor......Page 570
Solutions to Selected Exercises......Page 574
Further Reading......Page 588
B......Page 592
C......Page 593
E......Page 594
F......Page 595
G......Page 596
H......Page 597
M......Page 598
N......Page 599
P......Page 600
R......Page 601
S......Page 602
T......Page 603
Y......Page 604
Z......Page 605