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Lecture Notes in Mathematics

Quantum Potential Theory

Authors: Biane, P., Bouten, L., Cipriani, F., Konno, N., Xu, Q.

Editors: Franz, Uwe, Schuermann, Michael (Eds.)

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About this book

This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007.

Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.

Table of contents (7 chapters)

  • Introduction

    Pages 1-2

  • Potential Theory in Classical Probability

    Privault, Nicolas

    Pages 3-59

  • Introduction to Random Walks on Noncommutative Spaces

    Biane, Philippe

    Pages 61-116

  • Interactions between Quantum Probability and Operator Space Theory

    Xu, Quanhua

    Pages 117-159

  • Dirichlet Forms on Noncommutative Spaces

    Cipriani, Fabio

    Pages 161-276

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-540-69365-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-540-69364-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Potential Theory
Authors
Editors
  • Uwe Franz
  • Michael Schuermann
Series Title
Lecture Notes in Mathematics
Series Volume
1954
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69365-9
DOI
10.1007/978-3-540-69365-9
Softcover ISBN
978-3-540-69364-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 464
Number of Illustrations and Tables
18 b/w illustrations
Topics