Fock representation of the renormalized higher powers of White noise and the centreless Virasoro (or Witt)–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 centreless Virasoro (or Witt)–Zamolodchikov–w∞*-Lie algebra of conformal field theory and high-energy physics, was recently established in [5] based on results obtained in [3] and [4]. In the present paper, we show how the RHPWN Fock kernels must be truncated in order to be positive semi-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.