Integral Kernel Operators on Fock Space - Generalizations and Applications to Quantum Dynamics

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14 Citations (Scopus)

Abstract

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise ap]proach to quantum stochastic integrals is discussed and a quantum Hitsuda-Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.

Original languageEnglish
Pages (from-to)49-77
Number of pages29
JournalActa Applicandae Mathematicae
Volume47
Issue number1
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

Keywords

  • Fock space
  • Integral kernel operator
  • Quantum Langevin equation
  • Quantum stochastic integral
  • White noise distribution theory

ASJC Scopus subject areas

  • Applied Mathematics

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