L2-Representations of the Boson Fock Space

Asao Arai

Volkmar Liebscher

We show a simple way to generate a Markovian cocycle on H ⊗ Γ (L2(ℝ+, K)) from a semigroup of bounded operators on (H ⊗ L2(ℝ+, K)) ⊕ H ⊕ (H ⊗ L2(ℝ-, K) ⊗ L2(ℝ+, K))⊕ (H ⊗ L2(ℝ-, K)).

Kalyanapuram Rangachari Parthasarathy, Viakalathur Shankar Sunder

Xiaoshan Hu, Zhiyuan Huang, Xiangjun Wang

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)).