Contents
Part I SYMMETRY BREAKING IN CLASSICAL SYSTEMS
1 Symmetries of a Classical System . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2 Spontaneous Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3 Symmetries in Classical Field Theory . . . . . . . . . . . . . . . . . . . . . . . 11
4 General Properties of Solutions of Classical Field Equations . . . . . 17
5 Stable Structures, Hilbert Sectors, Phases . . . . . . . . . . . . . . . . . . . . 21
6 Stability Under Space Translations. Positive Energy . . . . . . . . . . . . 31
7 Noether Theorem and Symmetry Breaking . . . . . . . . . . . . . . . . . . . 35
8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
9 The Goldstone Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
10.1 Properties of the Free Wave Propagator . . . . . . . . . . . . . . . . . . 53
10.2 The Cauchy Problem for Small Times . . . . . . . . . . . . . . . . . . . 55
10.3 The Global Cauchy Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10.4 The Non-linear Wave Equation with Driving Term . . . . . . . . . . 59
10.5 Time-Independent Solutions Defining Physical Sectors . . . . . . . 60
Part I References
Part II SYMMETRY BREAKING IN QUANTUM SYSTEMS
11 Quantum Mechanics. Algebraic Structure and States . . . . . . . . . . . 73
12 Fock Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
13 Non-Fock Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
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