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Stochastic Processes in Quantum Physics

  • Book
  • © 2000

Overview

Authors:
  1. Masao Nagasawa

    1. Institute of Mathematics, University of Zürich, Zürich, Switzerland

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Part of the book series: Monographs in Mathematics (MMA, volume 94)

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Table of contents (16 chapters)

  1. Front Matter

    Pages N3-VII
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  2. Markov Processes

    • Masao Nagasawa
    Pages 1-26

  3. Time Reversal and Duality

    • Masao Nagasawa
    Pages 27-52

  4. Non-Relativistic Quantum Theory

    • Masao Nagasawa
    Pages 53-104

  5. Stationary Schrödinger Processes

    • Masao Nagasawa
    Pages 105-137

  6. Construction of the Schrödinger Processes

    • Masao Nagasawa
    Pages 139-184

  7. Markov Processes with Jumps

    • Masao Nagasawa
    Pages 185-229

  8. Relativistic Quantum Particles

    • Masao Nagasawa
    Pages 231-262

  9. Stochastic Differential Equations of Pure-Jumps

    • Masao Nagasawa
    Pages 263-285

  10. Variational Principle for Relativistic Quantum Particles

    • Masao Nagasawa
    Pages 287-313

  11. Time Dependent Subordination and Markov Processes with Jumps

    • Masao Nagasawa
    Pages 315-354

  12. Concave Majorants of Lévy Processes and the Light Cone

    • Masao Nagasawa
    Pages 355-388

  13. The Locality in Quantum Physics

    • Masao Nagasawa
    Pages 389-435

  14. Micro Statistical Theory

    • Masao Nagasawa
    Pages 437-460

  15. Processes on Open Time Intervals

    • Masao Nagasawa
    Pages 461-500

  16. Creation and Killing of Particles

    • Masao Nagasawa
    Pages 501-519

  17. The Itô Calculus

    • Masao Nagasawa
    Pages 521-571

  18. Back Matter

    Pages 573-598
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Keywords

About this book

"Stochastic Processes in Quantum Physics" addresses the question 'What is the mathematics needed for describing the movement of quantum particles', and shows that it is the theory of stochastic (in particular Markov) processes and that a relativistic quantum particle has pure-jump sample paths while sample paths of a non-relativistic quantum particle are continuous. Together with known techniques, some new stochastic methods are applied in solving the equation of motion and the equation of dynamics of relativistic quantum particles. The problem of the origin of universes is discussed as an application of the theory. The text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level, and some selected chapters can be used as (sub-)textbooks for advanced courses on stochastic processes, quantum theory and theoretical chemistry.

Reviews

"…the text is almost self-contained and requires only an elementary knowledge of probability theory at the graduate level. The book under review is recommended to mathematicians, physicists and graduate students interested in mathematical physics and stochastic processes. Furthermore, some selected chapters can be used as sub-textbooks for advanced courses on stochastic processes, quantum theory and quantum chemistry."

-ZAA

Authors and Affiliations

  • Institute of Mathematics, University of Zürich, Zürich, Switzerland

    Masao Nagasawa

Bibliographic Information

  • Book Title: Stochastic Processes in Quantum Physics

  • Authors: Masao Nagasawa

  • Series Title: Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8383-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6208-9Published: 01 May 2000

  • Softcover ISBN: 978-3-0348-9543-9Published: 28 October 2012

  • eBook ISBN: 978-3-0348-8383-2Published: 06 December 2012

  • Series ISSN: 1017-0480

  • Series E-ISSN: 2296-4886

  • Edition Number: 1

  • Number of Pages: VII, 598

  • Topics: Probability Theory and Stochastic Processes, Quantum Physics

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