Path Integrals and Hamiltonians
Principles and Methods

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

Belal E. Baaquie (Author)

9781107009790, Cambridge University Press

Hardback, published 27 March 2014

436 pages, 74 b/w illus.
24.4 x 17 x 2.4 cm, 0.89 kg

'The book is well written, in a compact style, but not stinting on clear explanations … Path Integrals and Hamiltonians looks like a very useful book, and I, for one, am very happy to have a copy.' Michael Berg, MAA Reviews

Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.

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
Index.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Physics [PH], Mathematics & science [P]