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

Luigi Accardi, Andreas Boukas

Published 2006-07-27, updated 2006-09-05Version 2

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.