RENORMALIZED HIGHER POWERS OF WHITE NOISE (RHPWN) AND CONFORMAL FIELD THEORY

Abstract

The Virasoro–Zamolodchikov *-Lie algebra w∞ 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∞ algebra. Arguments discussed at the end of this note suggest the conjecture that this inclusion is in fact an identification.