Path Integrals and Hamiltonians
Path Integrals and Hamiltonians
£135.00
GBPProviding 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.
- Gradually builds up from the simplest examples to a wide range of more complex scenarios
- Includes an in-depth analysis of a non-Hermitian Hamiltonian, demonstrating the ways and means by which quantum mechanics can be extended beyond the standard framework
- Demonstrates the emergence of quantum mathematics from the physical principles of quantum mechanics
Reviews & endorsements
'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
Product details
March 2014Hardback
9781107009790
436 pages
244 × 170 × 24 mm
0.89kg
74 b/w illus.
Available
Table of Contents
- 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.
