Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov -w∞ *-Lie algebra

Abstract

The identification of the ∗–Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro–Zamolodchikov–w1 ∗–Lie algebra of conformal field theory and high-energy physics, was recently established in [3] based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order ≥ 2 host the continuous binomial and beta processes