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

Luigi Accardi·Andreas Boukas
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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.

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Luigi Accardi, Andreas Boukas. 2006-09-05. The emergence of the Virasoro and $w_{\infty}$ algebras through the renormalized powers of quantum white noise. https://arxiv.org/abs/math-ph/0607062

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