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

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

2006-08-20

arxiv.org/abs/math-ph/0608047v2

Physics

Mathematical Physics

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

Scientific paper

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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