Path integrals and Hamiltonians : principles and methods / Belal E. Baaquie.

Includes bibliographical references and index.

1. Synopsis;
Part I. Fundamental Principles:
2. The mathematical structure of quantum mechanics;
3. Operators;
4. The Feynman path integral;
5. Hamiltonian mechanics;
6. Path integral quantization;

Part II. Stochastic Processes:
7. Stochastic systems;

Part III. Discrete Degrees of Freedom:
8. Ising model;
9. Ising model: magnetic field;
10. Fermions;

Part IV. Quadratic Path Integrals:
11. Simple harmonic oscillators;
12. Gaussian path integrals;

Part V. Action with Acceleration:
13. Acceleration Lagrangian;
14. Pseudo-Hermitian Euclidean Hamiltonian;
15. Non-Hermitian Hamiltonian: Jordan blocks;
16. The quartic potential: instantons;
17. Compact degrees of freedom;
18. Conclusions;
References;
Index.

This book introduces the powerful and flexible combination of Hamiltonian operators and path integrals in quantum mathematics.