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

TL;DR

This paper demonstrates that a renormalized algebra of higher powers of white noise encompasses a second quantized version of the $w_{}$ algebra, linking quantum probability with conformal field theory.

Contribution

It introduces a new renormalization method showing the RHPWN Lie algebra includes a second quantization of the $w_{}$ algebra, suggesting a deep connection between white noise analysis and conformal field theory.

Findings

RHPWN Lie algebra includes a second quantization of $w_{}$ algebra

New renormalization technique developed for white noise powers

Conjecture of algebraic identification between RHPWN and $w_{}$

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