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Modern Quantum Field Theory

Book Description

Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. 1. Introduction
    1. 1.1 Preface and conventions
    2. 1.2 Why quantum field theory?
  7. 2. Quantum theory of free scalar fields
    1. 2.1 Local fields
    2. 2.2 Problems for Chapter 2
  8. 3. Interacting field theory
    1. 3.1 Schwinger–Dyson equations and functional integrals
    2. 3.2 Functional integral solution of the SD equations
    3. 3.3 Perturbation theory
    4. 3.4 Connected and 1-P(article) I(rreducible) Green functions
    5. 3.5 Legendre’s trees
    6. 3.6 The Källen–Lehmann spectral representation
    7. 3.7 The scattering matrix and the LSZ formula
    8. 3.8 Problems for Chapter 3
  9. 4. Particles of spin 1, and gauge invariance
    1. 4.1 Massive spinning particles
    2. 4.2 Massless particles with helicity
    3. 4.3 Field theory for massive spin-1 particles
    4. 4.4 Problems for Chapter 4
  10. 5. Spin- ½ particles and Fermi statistics
    1. 5.1 Dirac, Majorana, and Weyl fields: discrete symmetries
    2. 5.2 The functional formalism for fermion fields
    3. 5.3 Feynman rules for Dirac fermions
    4. 5.4 Problems for Chapter 5
  11. 6. Massive quantum electrodynamics
    1. 6.1 Free the longitudinal gauge bosons!
    2. 6.2 Heavy-fermion production in electron–positron annihilation
    3. 6.3 Interaction with heavy fermions: particle paths and external fields
    4. 6.4 The magnetic moment of a weakly coupled charged particle
    5. 6.5 Problems for Chapter 6
  12. 7. Symmetries, Ward identities, and Nambu–Goldstone bosons
    1. 7.1 Space-time symmetries
    2. 7.2 Spontaneously broken symmetries
    3. 7.3 Nambu–Goldstone bosons in the semi-classical expansion
    4. 7.4 Low-energy effective field theory of Nambu–Goldstone bosons
    5. 7.5 Problems for Chapter 7
  13. 8. Non-abelian gauge theory
    1. 8.1 The non-abelian Higgs phenomenon
    2. 8.2 BRST symmetry
    3. 8.3 A brief history of the physics of non-abelian gauge theory
    4. 8.4 The Higgs model, duality, and the phases of gauge theory
    5. 8.5 Confinement of monopoles in the Higgs phase
    6. 8.6 The electro-weak sector of the standard model
    7. 8.7 Symmetries and symmetry breaking in the strong interactions
    8. 8.8 Anomalies
    9. 8.9 Quantization of gauge theories in the Higgs phase
    10. 8.10 Problems for Chapter 8
  14. 9. Renormalization and effective field theory
    1. 9.1 Divergences in Feynman graphs
    2. 9.2 Cut-offs
    3. 9.3 Renormalization and critical phenomena
    4. 9.4 The renormalization (semi-)group in field theory
    5. 9.5 Mathematical (Lorentz-invariant, unitary) quantum field theory
    6. 9.6 Renormalization of ϕ 4 field theory
    7. 9.7 Renormalization-group equations in dimensional regularization
    8. 9.8 Renormalization of QED at one loop
    9. 9.9 Renormalization-group equations in QED
    10. 9.10 Why is QED IR-free?
    11. 9.11 Coupling renormalization in non-abelian gauge theory
    12. 9.12 Renormalization-group equations for masses and the hierarchy problem
    13. 9.13 Renormalization-group equations for the S-matrix
    14. 9.14 Renormalization and symmetry
    15. 9.15 The standard model through the lens of renormalization
    16. 9.16 Problems for Chapter 9
  15. 10. Instantons and solitons
    1. 10.1 The most probable escape path
    2. 10.2 Instantons in quantum mechanics
    3. 10.3 Instantons and solitons in field theory
    4. 10.4 Instantons in the two-dimensional Higgs model
    5. 10.5 Monopole instantons in three-dimensional Higgs models
    6. 10.6 Yang–Mills instantons
    7. 10.7 Solitons
    8. 10.8 ’t Hooft–Polyakov monopoles
    9. 10.9 Problems for Chapter 10
  16. 11. Concluding remarks
  17. Appendix A. Books
  18. Appendix B. Cross sections
  19. Appendix C. Diracology
  20. Appendix D. Feynman rules
  21. Appendix E. Group theory and Lie algebras
  22. Appendix F. Everything else
  23. References
  24. Author index
  25. Subject index