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arXiv · 0706.3397

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

Luigi Accardi·Andreas Boukas
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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--$w_{\infty} *$--Lie algebra of conformal field theory and high-energy physics, was recently established in \cite{id} 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 $\geq 2$ host the continuous binomial and beta processes.

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Luigi Accardi, Andreas Boukas. 2007-06-26. Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra. https://doi.org/10.1088/1751-8113/41/30/304001

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