Nuclear Realization of Virasoro-Zamolodchikov-ω_∞ ★-Lie Algebras Through the Renormalized Higher Powers of Quantum Meixner White Noise

摘要

By using an appropriate one-mode type interacting Fock spaces, Γ_M(H), introduced in [1], we define a nuclear triple F_(M,θ)(ε) is contained in L~2(ε',Λ_M) is contained in F_(M,θ)*(ε) of test and generalized functions, with 9 being a suitable Young function. Moreover, we prove general characterization theorems for the fundamental nuclear spaces. For the applications, we introduce new renormalized products for the generators of the renormalized higher powers of white noise ★-Lie algebra and the Virasoro-Zamolodchikov-ω_∞ ★-Lie algebra. Then we show that these new renormalized products lead to nuclear realizations of these Lie algebras in terms of quantum Meixner white noise operators.