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
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