This book is intended to provide a general introduction to the physics of quantized fields and many-body physics. It is based on a two-semester sequence of courses taught at the University of Illinois at Urbana-Champaign at various times between 1985 and 1997. The students taking all or part of the sequence had interests ranging from particle and nuclear theory through quantum optics to condensed matter physics experiment.
The book does not cover as much ground as some texts. This is because I have tried to concentrate on the basic conceptual issues that many students find difficult. For a computation-method oriented course an instructor would probably wish to suplement this book with a more comprehensive and specialized text such as Peskin and Schroeder An Introduction to Quantum Field Theory, which is intended for particle theorists, or perhaps the venerable Quantum Theory of Many-Particle Systems by Fetter and Walecka.
Preface
1 Discrete Systems
1.1 One-Dimensional Harmonic Crystal
1.2 Continuum Limit
2 Relativistic Scalar Fields
2.1 Convcntions
2.2 The Klein-Gordon Equation
2.3 Symmetries and Noether's Theorem
3 Perturbation Theory
3.1 Interactions
3.2 Perturbation Theory
3.3 Wick's Theorem
4 Feynman Rules
4.1 Diagrams
4.2 Scattering Theory Preface
1 Discrete Systems
1.1 One-Dimensional Harmonic Crystal
1.2 Continuum Limit
2 Relativistic Scalar Fields
2.1 Convcntions
2.2 The Klein-Gordon Equation
2.3 Symmetries and Noether's Theorem
3 Perturbation Theory
3.1 Interactions
3.2 Perturbation Theory
3.3 Wick's Theorem
4 Feynman Rules
4.1 Diagrams
4.2 Scattering Theory
5 Loops, Unitarity, and Analyticity
5.1 Unitarity of the S Matrix
5.2 The Analytic S Matrix
5.3 Some Loop Diagrams
6 Formal Developments
6.1 Gell-Mann Low Theorem
6.2 Lehmann-Kaillen Spectral Representation
6.3 LSZ Reduction Formulae
7 Fermions
7.1 Dirac Equation
7.2 Spinors, Tensors, and Currents
7.3 Holes and the Dirac Sea
7.4 Quantization
8 QED
8.1 Quantizing Maxwell's Equations
8.2 Feynman Rules for QED
8.3 Ward Identity and Gauge Invariance
9 Electrons in Solids
10 Nonrelativistic Bosons
11 Finite Temperature
12 Path Integrals
13 Functional Methods
14 Path Integrals for Fermions
15 Lattice Field Theory
16 The Renormailzation Group
17 Fields and Renormalization
18 Large N Expansions
A Relativistic State Normalization
B The General Commutator
C Dimensional Regularization
D Spinors and the Principle of the Sextant
E Indefinite Metric
F Phonons and Momentum
G Determinants in Quantum Mechanics
Index
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