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Fock Space (2): Multiple Fock Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1538)

Abstract

From the algebraic point of view, a multiple Fock space over ℌ is nothing but a standard (symmetric or antisymmetric) Fock space over a direct sum of copies of ℌ,and new definitions are not necessary in principle. However, this chapter contains important new notation, and a few rather interesting constructions, like that of the “finite-temperature” (= extremal universally invariant) representations of the CCR. In classical probability, it corresponds to the passage from one-dimensional to several-dimensional Brownian motion, necessary for Ito’s theory of stochastic differential equations.

Keywords

  • Brownian Motion
  • Annihilation Operator
  • Exchange Operator
  • Test Vector
  • Initial Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1993 Springer-Verlag Berlin Heidelberg

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Meyer, PA. (1993). Fock Space (2): Multiple Fock Spaces. In: Quantum Probability for Probabilists. Lecture Notes in Mathematics, vol 1538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21558-6_5

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  • DOI: https://doi.org/10.1007/978-3-662-21558-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56476-8

  • Online ISBN: 978-3-662-21558-6

  • eBook Packages: Springer Book Archive