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Infinite Dimensional Analysis Quantum Probability and Related Topics

ANALYTIC CHARACTERIZATION OF ONE-MODE INTERACTING FOCK SPACE

Nobuhiro Asai

Published Sep 1, 2001• 13 citations
Publisher

Abstract

In this paper, we shall give the Segal–Bargmann representation space of the one-mode interacting Fock space. For this purpose, we shall define the generalized coherent vector associated with the Szegö–Jacobi parameters and introduce the associated integral transformation.
DOI
10.1142/s021902570100053x

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This article is concerned with compositions in the context of three standard quantizations in the framework of Fock spaces, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states also known as a Wick product and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for issues on time dynamics (see [ 29 , 13 ]). Anti-Wick quantization and Segal–Bargmann transforms are implied here for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick and Weyl symbols of the composition of two operators, we obtain an absolutely converging series and for the Weyl symbol, the remainder terms up to any orders of the expansion are controlled, still in the Fock space framework.