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Path Integrals and Hamiltonians: Principles and Methods

Autor Belal E. Baaquie
en Limba Engleză Hardback – 26 mar 2014
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.
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Specificații

ISBN-13: 9781107009790
ISBN-10: 1107009790
Pagini: 436
Ilustrații: 74 b/w illus.
Dimensiuni: 170 x 244 x 24 mm
Greutate: 0.91 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:New York, United States

Cuprins

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.

Recenzii

'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

Notă biografică


Descriere

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