Luigi Accardi, Andreas Boukas
Published 2006-08-20, updated 2006-09-05Version 2
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
Comments: Replaced title and abstract and corrected typos; To appear in Infinite Dimensional Analysis, Quantum Probability, and Related Topics (2006)
The emergence of the Virasoro and $w_{\infty}$ algebras through the renormalized powers of quantum white noise
The Heisenberg group and conformal field theory
Conformal Field Theory and Doplicher-Roberts Reconstruction
