Preface page xv
Acknowledgements xviii
1 Synopsis 1
Part one Fundamental principles 5
2 The mathematical structure of quantum mechanics 7
3 Operators 30
4 The Feynman path integral 61
5 Hamiltonian mechanics 80
6 Path integral quantization 105
Part two Stochastic processes 123
7 Stochastic systems 125
Part three Discrete degrees of freedom 159
8 Ising model 161
9 Ising model: magnetic field 180
10 Fermions 198
Part four Quadratic path integrals 223
11 Simple harmonic oscillator 225
12 Gaussian path integrals 251
Part five Action with acceleration 271
13 Acceleration Lagrangian 273
14 Pseudo-Hermitian Euclidean Hamiltonian 294
15 Non-Hermitian Hamiltonian: Jordan blocks 330
Part six Nonlinear path integrals 349
16 The quartic potential:instantons 351
17 Compact degrees of freedom 385
18 Conclusions 405
References 409
Index 413