  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.
