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Quantum Theory and Its Stochastic Limit

  • Book
  • © 2002

Overview

Authors:
  1. Luigi Accardi

    1. Centro Vito Volterra, Facolta di Economia, Università di Roma, Roma, Italy

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  2. Igor Volovich

    1. Steklov Mathematical Institute, Moscow, GSP-1, Russia

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  3. Yun Gang Lu

    1. Dipartimento di Matematica, Università degli Studi di Bari, Bari, Italy

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  • The first comprehensive monograph on this important new approach to quantum physics by one of the founders of the concept of stochastic limit in quantum theory.

  • Includes supplementary material: sn.pub/extras

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XX
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  2. Statement of the Problem and Simplest Models

    1. Front Matter

      Pages 1-1
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    2. Notations and Statement of the Problem

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 3-55

    3. Quantum Fields

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 57-84

    4. Those Kinds of Fields We Call Noises

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 85-111

    5. Open Systems

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 113-151

    6. Spin—Boson Systems

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 153-203

    7. Measurements and Filtering Theory

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 205-218

    8. Idea of the Proof and Causal Normal Order

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 219-236

    9. Chronological Product Approach to the Stochastic Limit

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 237-246

    10. Functional Integral Approach to the Stochastic Limit

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 247-254

    11. Low-Density Limit: The Basic Idea

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 255-260

    12. Six Basic Principles of the Stochastic Limit

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 261-282

  3. Strongly Nonlinear Regimes

    1. Front Matter

      Pages 283-283
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    2. Particles Interacting with a Boson Field

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 285-350

    3. The Anderson Model

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 351-368

    4. Field—Field Interactions

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 369-390

  4. Estimates and Proofs

    1. Front Matter

      Pages 391-391
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    2. Analytical Theory of Feynman Diagrams

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 393-451

    3. Term-by-Term Convergence

      • Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 453-460
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Keywords

About this book

Nowadays it is becoming clearer and clearer that, in the description of natural phenomena, the triadic scheme - microseopie, mesoscopic, macroscopic - is only a rough approximation and that there are many levels of description, probably an infinite hierarchy, in which the specific properties of a given level express some kind of cumulative or collective behaviour of properties or sys­ tems corresponding to the lower levels. One of the most interesting challenges for contemporary natural sciences is the comprehension of the connections among these different levels of description of reality and the deduction of the laws of higher levels in this hierarchy from basic laws corresponding to lower levels. Since these cumulative or collective phenomena are, typically, nonlin­ ear effects, the transition from this general program to concrete scientific achievements requires the developement of techniques which allow physical information to be extracted from nonlinear quantum systems. Explicitly in­ tegrable examples of such systems are rare, and the most interesting physical phenomena are not captured by them. Even in the case of linear systems the fact that an explicit solution is formally available is often useless, since it is impossible to interpret interesting physical phenomena from it.

Reviews

"The authors have produced a very important and detailed book on the subject of the stochastic limit of quantum field theory. In particular, they formulate the stochastic limit in the framework of an algebraic central limit theory using the sort of scaling limits encountered in quantum transport phenomena. [...] The book is well written and covers many related problems [...] The audience will be mathematical and theoretical physicists. The authors are to be congratulated for showing the power and range of application of quantum probability to quantum physics." (Mathematical Reviews 2003h)

Authors and Affiliations

  • Centro Vito Volterra, Facolta di Economia, Università di Roma, Roma, Italy

    Luigi Accardi

  • Steklov Mathematical Institute, Moscow, GSP-1, Russia

    Igor Volovich

  • Dipartimento di Matematica, Università degli Studi di Bari, Bari, Italy

    Yun Gang Lu

Bibliographic Information

  • Book Title: Quantum Theory and Its Stochastic Limit

  • Authors: Luigi Accardi, Igor Volovich, Yun Gang Lu

  • DOI: https://doi.org/10.1007/978-3-662-04929-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-540-41928-0Published: 07 August 2002

  • Softcover ISBN: 978-3-642-07543-8Published: 07 December 2010

  • eBook ISBN: 978-3-662-04929-7Published: 14 March 2013

  • Edition Number: 1

  • Number of Pages: XX, 474

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics, Probability Theory and Stochastic Processes

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