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Quantum Field Theory, 2nd Edition

ISBN: 978-0-471-49683-0
492 pages
May 2010
Quantum Field Theory, 2nd Edition (0471496839) cover image
Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics.

The three main objectives of the book are to:

Explain the basic physics and formalism of quantum field theory

To make the reader proficient in theory calculations using Feynman diagrams

To introduce the reader to gauge theories, which play a central role in elementary particle physics.

Thus, the first ten chapters deal with QED in the canonical formalism, and are little changed from the first edition. A brief introduction to gauge theories (Chapter 11) is then followed by two sections, which may be read independently of each other. They cover QCD and related topics (Chapters 12-15) and the unified electroweak theory (Chapters 16 – 19) respectively. Problems are provided at the end of each chapter.

New to this edition:

Five new chapters, giving an introduction to quantum chromodynamics and the methods used to understand it: in particular, path integrals and the renormalization group.

The treatment of electroweak interactions has been revised and updated to take account of more recent experiments.

See More
Preface.

Notes.

1 Photons and the Electromagnetic Field.

1.1 Particles and Fields.

1.2 The Electromagnetic Field in the Absence of Charges.

1.3 The Electric Dipole Interaction.

1.4 The Electromagnetic Field in the Presence of Charges.

1.5 Appendix: The Schrödinger, Heisenberg and Interaction Pictures.

Problems.

2 Lagrangian Field Theory.

2.1 Relativistic Notation.

2.2 Classical Lagrangian Field Theory.

2.3 Quantized Lagrangian Field Theory.

2.4 Symmetries and Conservation Laws.

Problems.

3 The Klein–Gordon field.

3.1 The Real Klein–Gordon Field.

3.2 The Complex Klein–Gordon Field.

3.3 Covariant Commutation Relations.

3.4 The Meson Propagator.

Problems.

4 The Dirac Field.

4.1 The Number Representation for Fermions.

4.2 The Dirac Equation.

4.3 Second Quantization.

4.4 The Fermion Propagator.

4.5 The Electromagnetic Interaction and Gauge Invariance.

Problems.

5 Photons: Covariant Theory.

5.1 The Classical Fields.

5.2 Covariant Quantization.

5.3 The Photon Propagator.

Problems.

6 The S-Matrix Expansion.

6.1 Natural Dimensions and Units.

6.2 The S-Matrix Expansion.

6.3 Wick’s Theorem.

7 Feynman Diagrams and Rules in QED.

7.1 Feynman Diagrams in Configuration Space.

7.2 Feynman Diagrams in Momentum Space.

7.3 Feynman Rules for QED.

7.4 Leptons.

Problems.

8 QED Processes in Lowest Order.

8.1 The Cross-Section.

8.2 Spin Sums.

8.3 Photon Polarization Sums.

8.4 Lepton Pair Production in (eþe_) Collisions.

8.5 Bhabha Scattering.

8.6 Compton Scattering.

8.7 Scattering by an External Field.

8.8 Bremsstrahlung.

8.9 The Infra-Red Divergence.

Problems.

9 Radiative Corrections.

9.1 The Second-Order Radiative Corrections of QED.

9.2 The Photon Self-Energy.

9.3 The Electron Self-Energy.

9.4 External Line Renormalization.

9.5 The Vertex Modification.

9.6 Applications.

9.7 The Infra-Red Divergence.

9.8 Higher-Order Radiative Corrections.

9.9 Renomalizability.

Problems.

10 Regularization.

10.1 Mathematical Preliminaries.

10.2 Cut-Off Regularization: The Electron Mass Shift.

10.3 Dimensional Regularization.

10.4 Vacuum Polarization.

10.5 The Anomalous Magnetic Moment.

Problems.

11 Gauge Theories.

11.1 The Simplest Gauge Theory: QED.

11.2 Quantum Chromodynamics.

11.3 Alternative Interactions?.

11.4 Appendix: Two Gauge Transformation Results.

Problems.

12 Field Theory Methods.

12.1 Green Functions.

12.2 Feynman Diagrams and Feynman Rules.

12.3 Relation to S-Matrix Elements.

12.4 Functionals and Grassmann Fields.

12.5 The Generating Functional.

Problems.

13 Path Integrals.

13.1 Functional Integration.

13.2 Path Integrals.

13.3 Perturbation Theory.

13.4 Gauge Independent Quantization?.

Problems.

14 Quantum Chromodynamics.

14.1 Gluon Fields.

14.2 Including Quarks.

14.3 Perturbation Theory.

14.4 Feynman Rules for QCD.

14.5 Renormalizability of QCD.

Problems.

15 Asymptotic Freedom.

15.1 Electron-Positron Annihilation.

15.2 The Renormalization Scheme.

15.3 The Renormalization Group.

15.4 The Strong Coupling Constant.

15.5 Applications.

15.6 Appendix: Some Loop Diagrams in QCD.

Problems.

16 Weak Interactions.

16.1 Introduction.

16.2 Leptonic Weak Interactions.

16.3 The Free Vector Boson Field.

16.4 The Feynman Rules for the IVB Theory.

16.5 Decay Rates.

16.6 Applications of the IVB Theory.

16.7 Neutrino Masses.

16.8 Difficulties with the IVB Theory.

Problems.

17 A Gauge Theory of Weak Interactions.

17.1 QED Revisited.

17.2 Global Phase Transformations and Conserved Weak Currents.

17.3 The Gauge-Invariant Electro-Weak Interaction.

17.4 Properties of the Gauge Bosons.

17.5 Lepton and Gauge Boson Masses.

18 Spontaneous Symmetry Breaking.

18.1 The Goldstone Model.

18.2 The Higgs Model.

18.3 The Standard Electro-Weak Theory.

19 The Standard Electro–weak Theory.

19.1 The Lagrangian Density in the Unitary Gauge.

19.2 Feynman Rules.

19.3 Elastic Neutrino–Electron Scattering.

19.4 Electron–Positron Annihilation.

19.5 The Higgs Boson.

Problems.

Appendix A.

Appendix B.

Index.

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  • Five new chapters, giving an introduction to quantum chromodynamics and the methods used to understand it: in particular, path integrals and the renormalization group.

  • The treatment of electroweak interactions has been revised and updated to take account of more recent experiments.

 

See More
  • This timely revision of a classic text includes vital new coverage on QCD, path integrals, and renormalization group.
  • Carefully structured, introducing mathematical formalism from first principles.

 

 

See More
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