Infinite Dimensional Analysis Quantum Probability and Related Topics

L2(E*, μ)-WEYL REPRESENTATIONS

Xiaoshan Hu, Zhiyuan Huang, Xiangjun Wang

Published Dec 1, 2002• 0 citations

Abstract

For the canonical commutation relations in infinite dimensions, we offer an explicit direct construction of Weyl representations Wϕ generated from the Fock representation by any ϕ ∈ L2(E*, μ, R) over the Q-space (E*, μ). Moreover, we obtain that, for any ϕ, ψ ∈ L2(E*, μ,R), Wϕ+ψ and Wϕ are unitarily equivalent, proving a conjecture posed by Robinson in Ref. 2. Our construction employs Wiener–Itô decomposition of the space L2(E*, μ, R) (respectively L2(E*, μ, C)).

DOI: 10.1142/s0219025702000985

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