1 Introduction
1.1 Preface and conventions
1.2 Why quantum field theory?
2 quantum theory of free scalar fields
2.1 Local fields
2.2 Problems for Chapter 2
3 Interacting field theory
3.1 Schwinger-Dyson equations and functional integrals
3.2 Functional integral solution of he SD equations
3.3 Perturbation theory
3.4 Connected and 1-P(article) I(rreducible) Green functions
3.5 Legendre's trees
3.6 The ICdillen Lehmann spectral representation
3.7 The scattering matrix and the LSZ formula
3.8 Problems for Chapter 3
4 Particles of spin 1, and gauge invariance
4.1 Massive spinning particles
4.2 Massless particles with helicity
4.3 Field theory for massive spin-1 particles
4.4 Problems for Chapter 4
5 Spin-particles and Fermi statistics
5.1 Dirac, Majorana, and Weyl fields: discrete symmetries
5.2 The functional formalism for fermion fields
5.3 Feynman rules for Dirac fermions
5.4 Problems for Chapter 5
6 Massive quantum electrodynamics
6.1 Free the longitudinal gauge bosons!
6.2 Heavy-fermion production in electron-positron annihilation
6.3 Interaction with heavy fermions: particle paths and external fields
6.4 The magnetic moment of a weakly coupled charged particle
6.5 Problems for Chapter 6
7 Symmetries, Ward identities, and Nambu-Goldstone bosons
7.1 Space-time symmetries
7.2 Spontaneously broken symmetries
7.3 Nambu-Goldstone bosons in the semi-classical expansion
7.4 Low-energy effective field theory of Nambu Goldstone bosons
7.5 Problems for Chapter 7
8 Non-abelian gauge theory
8.l The non-abelian Higgs phenomenon
8.2 BRST symmetry
8.3 A brief history of the physics of non-abelian gauge theory
8.4 The Higgs model, duality, and the phases of gauge theory
8.5 Confinement ofmonopoles in the Higgs phase
8.6 The electro-weak sector of the standard model
8.7 Symmetries and symmetry breaking in the strong interactions
8.8 Anomalies
8.9 Quantization of gauge theories in the Higgs phase
8.10 Problems for Chapter 8
9 Renormalizati0n and effective field theory
9.1 Divergences in Feynman graphs
9.2 Cut-offs
9.3 Renormalization and critical phenomena
9.4 The renormalization (semi-)group in field theory
9.5 Mathematical (Lorentz-invariant, unitary) quantum field theory
9.6 Renormalization of 4 field theory
9.7 Renormalization-group equations in dimensional regularization
9.8 Renormalization of QED at one loop
9.9 Renormalization-group equations in QED
9.10 Whyis QED IR-free?
9.11 Coupling renormalization in non-abelian gauge theory
9.12 Renormalization-group equatinns for masses and the hierarchy problem
9.13 Renormalization-group equations for the S-matrix
9.14 Renormalization and symmetry
9.15 The standard model through the lens of renormalizatinn
9.16 Problems for Chapter 9
10 Instantons and solitons
100.1 The most probable escape path
10.2 Instantons in quantum mechanics
10.3 Instantons and solitons in field theory
10.4 Instantons in the two-dimensional Higgs model
10.5 Monopole instantons in three-dimensional Higgs models
10.6 Yan Mills instantons
10.7 Solitons
10.8 Hooft Polyakov monopoles
10.9 Problems for Chapter 10
11 Concluding remarks
Appendix A Books
Appendix B Cross sections
Appendix C Diracology
Appendix D Feynman rules
Appendix E Group theory and Lie algebras
Appendix F Everything else
References
Author index
Subiect index
