本书首先介绍了路径积分和哈密顿量的基本原理。继而，本书讨论了这些原理在广泛的领域，包括量子力学、固体物理、统计力学、量子场论、超弦理论等物理的应用。本书还探讨了路径积分及哈密顿量在高分子、生物学、化学等领域的应用。

Preface
Acknowledgements
1 Synopsis
Part one Fundamental principles
2 The mathernatieal structure of quantum mechanics
2.1 The Copenhagen quantum postulate
2.2 The superstructure of quantum mechanics
2.3 Degree of freedom space F
2.4 State space V(F)
2.4.1 Hilbert space
2.5 Operators O(F)
2.6 The process of measurement
2.7 The Schrodinger differential equation
2.8 Heisenberg operator approach
2.9 Dirac-Feynman path integral formulation
2.10 Three formulations of quantum mechanics
2.11 Quantum entity
2.12 Summary
3 Operators
3.1 Continuous degree of freedom
3.2 Basis states for state space
3.3 Hermitian operators
3.3.1 Eigenfunctions; completeness
3.3.2 Hamiltonian for a periodic degree of freedom
3.4 Position and momentum operators h and/
3.4.1 Momentum operator
3.5 Weyl operators
3.6 Quantum numbers; commuting operator
3.7 Heisenberg commutation equation
3.8 Unitary representation of Heisenberg algebra
3.9 Density matrix: pure and mixed states
3.10 Self-adjoint operators
3.10.1 Momentum operator on finite interval
3.11 Self-adjoint domain
3.11.1 Real eigenvalues
3.12 Hamiltonian's self-adjoint extension
3.12.1 Delta function potential
3.13 Fermi pseudo-potential
3.14 Summary
4 The Feynman path integral
4.1 Probability amplitude and time evolution
4.2 Evolution kernel
4.3 Superposition: indeterminate paths
4.4 The Dirac-Feynman formula
4.5 The Lagrangian
4.5.1 Infinite divisibility of quantum paths
4.6 The Feynman path integral
4.7 Path integral for evolution kernel
4.8 Composition rule for probability amplitudes
4.9 Summary
5 Hamiltonian mechanics
5.1 Canonical equations
5.2 Symmetries and conservation laws
5.3 Euclidean Lagrangian and Hamiltonian
5.4 Phase space path integrals
5.5 Poisson bracket
5.6 Commutation equations
5.7 Dirac bracket and constrained quantization
5.7.1 Dirac bracket for two constraints
5.8 Free particle evolution kernel
5.9 Hamiltonian and path integral
5.10 Coherent states
5.11 Coherent state vector
5.12 Completeness equation: over-complete
5.13 Operators; normal ordering
……
6 Path integral quantization
Part two Stochastic processes
7 Stochastic systems
Part three Discrete degrees of freedom
8 Ising model
9 Ising model: magnetic field
10 Fermions
Part four Quadratic path integrals
11 Simple harmonic oscillator
12 Gaussian path integrals
Part five Action with acceleration
13 Acceleration Lagrangian
14 Pseudo-Hermitian Euclidean Hamiltonian
15 Non-Hermitian Hamiltonian: Jordan blocks
Part six Nonlinear path integrals
16 The quartic potential: instantons
17 Compact degrees of freedom
18 Conclusions
References
Index