Mathematics and its Applications

Gleason's Theorem and Its Applications

Authors: Dvurecenskij, Anatolij

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About this book

For many years physics and mathematics have had a fruitful influence on one another. Classical mechanics and celestial mechanics have produced very deep problems whose solutions have enhanced mathematics. On the other hand, mathematics itself has found interesting theories which then (sometimes after many years) have been reflected in physics, confirming the thesis that nothing is more practical than a good theory. The same is true for the younger physical discipline -of quantum mechanics. In the 1930s two events, not at all random, became: The mathematical back­ grounds of both quantum mechanics and probability theory. In 1936, G. Birkhoff and J. von Neumann published their historical paper "The logic of quantum mechanics", in which a quantum logic was suggested. The mathematical foundations of quantum mechanics remains an outstanding problem of mathematics, physics, logic and philosophy even today. The theory of quantum logics is a major stream in this axiomatical knowledge river, where L(H), the system of all closed subspaces of a Hilbert space H, due to J. von Neumann, plays an important role. When A.M. Gleason published his solution to G. Mackey's problem showing that any state (= probability measure) corresponds to a density operator, he probably did not anticipate that his solution would become a cornerstone of ax iomati cal theory of quantum mechanics nor that it would provide many interesting applications to mathematics.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-94-015-8222-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-0-7923-1990-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-90-481-4209-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Gleason's Theorem and Its Applications
Authors
Series Title
Mathematics and its Applications
Series Volume
60
Copyright
1993
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
Distribution Rights
No sales rights in Czech Republik, Slovakia
eBook ISBN
978-94-015-8222-3
DOI
10.1007/978-94-015-8222-3
Hardcover ISBN
978-0-7923-1990-0
Softcover ISBN
978-90-481-4209-5
Series ISSN
0169-507X
Edition Number
1
Number of Pages
XVI, 325
Topics