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Path Integrals and Hamiltonians
Principles and Methods

£113.00

  • Date Published: March 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107009790

£ 113.00
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  • 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.

    • 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
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    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

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    Product details

    • Date Published: March 2014
    • format: Hardback
    • isbn: 9781107009790
    • length: 436 pages
    • dimensions: 244 x 170 x 24 mm
    • weight: 0.89kg
    • contains: 74 b/w illus.
    • availability: 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.

  • Author

    Belal E. Baaquie, National University of Singapore
    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).

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