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Renormalized Higher Powers of White Noise (RHPWN) and Conformal Field Theory

Luigi Accardi·Andreas Boukas
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Abstract

The Virasoro--Zamolodchikov Lie algebra $w_{\infty}$ has been widely studied in string theory and in conformal field theory, motivated by the attempts of developing a satisfactory theory of quantization of gravity. The renormalized higher powers of quantum white noise (RHPWN) *-Lie algebra has been recently investigated in quantum probability, motivated by the attempts to develop a nonlinear generalization of stochastic and white noise analysis. We prove that, after introducing a new renormalization technique, the RHPWN Lie algebra includes a second quantization of the $w_{\infty}$ algebra. Arguments discussed at the end of this note suggest the conjecture that this inclusion is in fact an identification

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Luigi Accardi, Andreas Boukas. 2006-09-05. Renormalized Higher Powers of White Noise (RHPWN) and Conformal Field Theory. https://arxiv.org/abs/math-ph/0608047

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