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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114997We 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 2006Mathematical Physics81S05, 60H40The emergence of the Virasoro and $w_{\infty}$ algebras through the renormalized powers of quantum white noisetext