Skip to main content

Fock Space (1)

  • Chapter
  • 782 Accesses

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

Abstract

The preceding chapters dealt with the non-commutative analogues of discrete r.v.’s, then of real valued r.v.’s, and we now begin to discuss stochastic processes. We start with the description of Fock space (symmetric and antisymmetric) as it is usually given in physics books. Then we show that boson Fock space is isomorphic to the L 2 space of Wiener measure, and interpret on Wiener space the creation, annihilation and number operators. We proceed with the Poisson interpretation of Fock space, and the operator interpretation of the Poisson multiplication. We conclude with multiplication formulas, and the useful analogy with “toy Fock space” in chapter II, which leads to the antisymmetric (Clifford) multiplications. All these operations are special cases of Maassen’s kernel calculus (§4).

Keywords

  • Annihilation Operator
  • Stochastic Integral
  • Wiener Space
  • Weyl Operator
  • Clifford Multiplication

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Meyer, PA. (1993). Fock Space (1). In: Quantum Probability for Probabilists. Lecture Notes in Mathematics, vol 1538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21558-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21558-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56476-8

  • Online ISBN: 978-3-662-21558-6

  • eBook Packages: Springer Book Archive