Springer Monographs in Mathematics

Mathematical Topics Between Classical and Quantum Mechanics

Authors: Landsman, Nicholas P.

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About this book

Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan­ tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan­ tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "algebraic" and "geometric" with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper­ ator algebras, and their state spaces, which is based on this relationship.

Table of contents (5 chapters)

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-1-4612-1680-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-0-387-98318-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4612-7242-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Topics Between Classical and Quantum Mechanics
Authors
Series Title
Springer Monographs in Mathematics
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1680-3
DOI
10.1007/978-1-4612-1680-3
Hardcover ISBN
978-0-387-98318-9
Softcover ISBN
978-1-4612-7242-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XIX, 529
Topics