Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra

摘要

The identification of the $*$--Lie algebra of the renormalized higher powersof white noise (RHPWN) and the analytic continuation of the second quantizedVirasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra of conformal field theoryand high-energy physics, was recently established in \cite{id} based on resultsobtained in [1] and [2]. In the present paper we show how the RHPWN Fockkernels must be truncated in order to be positive definite and we obtain a Fockrepresentation of the two algebras. We show that the truncated renormalizedhigher powers of white noise (TRHPWN) Fock spaces of order $\geq 2$ host thecontinuous binomial and beta processes.