Preface
1 From particles to fields
1.1 Classical harmonic chain: phonons
1.2 Functional analysis and variational principles
1.3 Maxwell's equations as a variational principle
1.4 Quantum chain
1.5 Quantum electrodynamics
1.6 Noether's theorem
1.7 Summary and outlook
1.8 Problems
2 Second quantization
2.1 Introduction to second quantization
2.2 Applications of second quantization
2.3 Summary and outlook
2.4 Problems
3 Feymnan path integral
3.1 The path integral: general formalism
3.2 Construction of the path integral
3.3 Applications of the Feynman path integral
3.4 Summary and outlook
3.5 Problems
4 Functional field integral
4.1 Construction of the many-body path integral
4.2 Field integral for the quantum partition function
4.3 Field theoretical bosonization: a case study
4.4 Summary and outlook
4.5 Problems
5 Perturbation theory
5.1 General structures and low-order expansions
5.2 Ground state energy of the interacting electron gas
5.3 Infinite-order expansions
5.4 Summary and outlook
5.5 Problems
6 Broken symmetry and collective phenomena
6.1 Mean-field theory
6.2 Plasma theory of the interacting electron gas
6.3 Bose-Einstein condensation and superfluidity
6.4 Superconductivity
6.5 Field theory of the disordered electron gas
6.6 Summary and outlook
6.7 Problems
7 Response functions
7.1 Crash course in modem experimental techniques
7.2 Linear response theory
7.3 Analytic structure of correlation functions
7.4 Electromagnetic linear response
7.5 Summary and outlook
7.6 Problems
8 The renormalization group
8.1 The one-dimensional Ising model
8.2 Dissipative quantum tunneling
8.3 Renormalization group: generaltheory
8.4 RG analysis of the ferromagnetic transition
8.5 RG analysis of the nonlinear o'-model
8.6 Berezinskii-Kosterlitz-Thouless transition
8.7 Summary and outlook
8.8 Problems
9 Topology
9.1 Example: particle on a ring
9.2 Homotopy
9.3 θ-Terms
9.4 Wess-Zumino terms
9.5 Chern-Simons terms
9.6 Summary and outlook
9.7 Problems
Index
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