Quantum Field Theory

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ISBN: 9780521478144 | 0521478146
Cover: Paperback
Copyright: 6/13/1996

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This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of 'topological' objects in field theory and, new to this edition, a chapter devoted to supersymmetry.

Preface to the first edition

xvii

Preface to the second edition

xix

Introduction: synopsis of particle physics

(24)

Quantum field theory

(1)

Gravitation

(1)

Strong interactions

(1)

Weak interactions

(1)

Leptonic quantum numbers

(2)

Hadronic quantum numbers

(1)

Resonances

(1)

The quark model

(3)

SU(2), SU(3), SU(4), ...

(3)

Dynamical evidence for quarks

(3)

Colour

(4)

QCD

(1)

Weak interactions

(1)

Guide to further reading

(1)

Single-particle relativistic wave equations

(54)

Relativistic notation

(2)

Klein--Gordon equation

(2)

Dirac equation

(13)

SU(2) and the rotation group

(6)

SL(2, C) and the Lorentz group

(6)

Prediction of antiparticles

(4)

Construction of Dirac spinors: algebra of γ matrices

(6)

Non-relativistic limit and the electron magnetic moment

(3)

The relevance of the Poincare group: spin operators and the zero mass limit

(9)

Maxwell and Proca equations

(5)

Maxwell's equations and differential geometry

(10)

Summary

(1)

Guide to further reading

(2)

Lagrangian formulation, symmetries and gauge fields

(47)

Lagrangian formulation of particle mechanics

(1)

The real scalar field: variational principle and Noether's theorem

(9)

Complex scalar fields and the electromagnetic field

(8)

Topology and the vacuum: the Bohm--Aharonov effect

(7)

The Yang--Mills field

105

(7)

The geometry of gauge fields

112

(14)

Summary

124

(1)

Guide to further reading

125

(1)

Canonical quantisation and particle interpretation

126

(28)

The real Klein--Gordon field

126

(9)

The complex Klein--Gordon field

135

(2)

The Dirac field

137

(3)

The electromagnetic field

140

(10)

Radiation gauge quantisation

142

(3)

Lorentz gauge quantisation

145

(5)

The massive vector field

150

(4)

Summary

152

(1)

Guide to further reading

153

(1)

Path integrals and quantum mechanics

154

(28)

Path-integral formulation of quantum mechanics

154

(7)

Perturbation theory and the S matrix

161

(9)

Coulomb scattering

170

(2)

Functional calculus: differentiation

172

(2)

Further properties of path integrals

174

(8)

Appendix: some useful integrals

179

(2)

Summary

181

(1)

Guide to further reading

181

(1)

Path-integral quantisation and Feynman rules: scalar and spinor fields

182

(58)

Generating functional for scalar fields

182

(4)

Functional integration

186

(3)

Free particle Green's functions

189

(7)

Generating functionals for interacting fields

196

(4)

&phis;4 theory

200

(7)

Generating functional

200

(2)

2-point function

202

(2)

4-point function

204

(3)

Generating functional for connected diagrams

207

(3)

Fermions and functional methods

210

(7)

The S matrix and reduction formula

217

(7)

Pion--nucleon scattering amplitude

224

(8)

Scattering cross section

232

(8)

Summary

238

(1)

Guide to further reading

239

(1)

Path-integral quantisation: gauge fields

240

(42)

Propagators and gauge conditions in QED

240

(5)

Photon propagator -- canonical formalism

240

(2)

Photon propagator -- path-integral method

242

(1)

Gauge-fixing terms

242

(1)

Propagator for transverse photons

243

(2)

Non-Abelian gauge fields and the Faddeev--Popov method

245

(10)

Feynman rules in the Lorentz gauge

250

(4)

Gauge-field propagator in the axial gauge

254

(1)

Self-energy operator and vertex function

255

(8)

Geometrical interpretation of the Legendre transformation

260

(2)

Thermodynamic analogy

262

(1)

Ward--Takahashi identities in QED

263

(7)

Becchi--Rouet--Stora transformation

270

(3)

Slavnov--Taylor identities

273

(3)

A note on ghosts and unitarity

276

(6)

Summary

280

(1)

Guide to further reading

281

(1)

Spontaneous symmetry breaking and the Weinberg--Salam model

282

(26)

What is the vacuum?

282

(5)

The Goldstone theorem

287

(6)

Spontaneous breaking of gauge symmetries

293

(3)

Superconductivity

296

(2)

The Weinberg--Salam model

298

(10)

Summary

306

(1)

Guide to further reading

307

(1)

Renormalisation

308

(82)

Divergences in &phis;4 theory

308

(5)

Dimensional analysis

311

(2)

Dimensional regularisation of &phis;4 theory

313

(5)

Loop expansion

317

(1)

Renormalisation of &phis;4 theory

318

(6)

Counter-terms

321

(3)

Renormalisation group

324

(5)

Divergences and dimensional regularisation of QED

329

(8)

1-loop renormalisation of QED

337

(10)

Anomalous magnetic moment of the electron

343

(2)

Asymptotic behaviour

345

(2)

Renormalisability of QED

347

(6)

Asymptotic freedom of Yang--Mills theories

353

(9)

Renormalisation of pure Yang--Mills theories

362

(4)

Chiral anomalies

366

(9)

Cancellation of anomalies

373

(2)

Renormalisation of Yang--Mills theories with spontaneous symmetry breakdown

375

(15)

't Hooft's gauges

375

(2)

The effective potential

377

(3)

Loop expansion of the effective potential

380

(2)

Appendix A: integration in d dimensions

382

(3)

Appendix B: the gamma function

385

(2)

Summary

387

(1)

Guide to further reading

388

(2)

Topological objects in field theory

390

(36)

The sine--Gordon kink

391

(4)

Vortex lines

395

(7)

The Dirac monopole

402

(4)

The 't Hooft--Polyakov monopole

406

(8)

Instantons

414

(12)

Quantum tunnelling, &thetas;-vacua and symmetry breaking

420

(4)

Summary

424

(1)

Guide to further reading

424

(2)

Supersymmetry

426

(50)

Introduction

426

(1)

Lorentz transformations: Dirac, Weyl and Majorana spinors

427

(13)

Some further relations

436

(4)

Simple Lagrangian model

440

(6)

Digression: Fierz rearrangement formula

444

(2)

Simple Lagrangian model (cont.): closure of commutation relations

446

(6)

Mass term

450

(2)

Towards a super-Poincare algebra

452

(7)

Superspace

459

(5)

Superfields

464

(6)

Chiral superfield

467

(3)

Recovery of the Wess--Zumino model

470

(6)

Appendix: some 2-spinor conventions

473

(2)

Summary

475

(1)

Guide to further reading

475

(1)

References

476

(6)

Index

482

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Quantum Field Theory

Summary

Table of Contents

Supplemental Materials