Path Integrals and Hamiltonians

Path Integrals and Hamiltonians : Principles and Methods

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Description

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 Schrodinger 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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 74 b/w illus.
  • 1139698605
  • 9781139698603

About Belal E. Baaquie

Belal E. Baaquie is a Professor of Physics at the National University of Singapore, specializing in quantum field theory, quantum mathematics and quantum finance. He is the author of Quantum Finance (2004), Interest Rates and Coupon Bonds in Quantum Finance (2009), The Theoretical Foundations of Quantum Mechanics (2013) and co-author of Exploring Integrated Science (2010).show more

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.show more

Review quote

'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 Reviewsshow more