The emergence of the Virasoro and $w_{\infty }$ algebras through the renormalized powers of quantum white noise

Abstract

We introduce a new renormalization for the powers of the Dirac delta function. We show that this new renormalization leads to a second quantized version of the Virasoro sector $w_{\infty }$ of the extended conformal algebra with infinite symmetries $W_{\infty }$ of Conformal Field Theory. In particular we construct a white noise (boson) representation of the $w_{\infty }$ generators and commutation relations and of their second quantization.

corrected typos; Submitted to International Journal of Mathematics and Computer Science in June 2006

Cited by in corpus (2)

• Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
• Renormalized Higher Powers of White Noise and the Virasoro-Zamolodchikov-$w_{\infty }$ Algebra