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

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

Replaced title and abstract and corrected typos; To appear in Infinite Dimensional Analysis, Quantum Probability, and Related Topics (2006)