The identification of the ∗–Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro–Zamolodchikov–w1 ∗–Lie algebra of conformal field theory and high-energy physics, was recently established in [3] based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order ≥ 2 host the continuous binomial and beta processes.

Bouka, A., & Accardi, L. (2007). Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov -w∞ *-Lie algebra.

Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov -w∞ *-Lie algebra

ACCARDI, LUIGI
2007-06

Abstract

The identification of the ∗–Lie algebra of the renormalized higher powers of white noise (RHPWN) and the analytic continuation of the second quantized Virasoro–Zamolodchikov–w1 ∗–Lie algebra of conformal field theory and high-energy physics, was recently established in [3] based on results obtained in [1] and [2]. In the present paper we show how the RHPWN Fock kernels must be truncated in order to be positive definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of white noise (TRHPWN) Fock spaces of order ≥ 2 host the continuous binomial and beta processes.
renormalized powers of white noise
second quantization
w1-algebra
Virasoro algebra
Zamolodchikov algebra
Fock space
moment systems
continuous binomial distribution
Bouka, A., & Accardi, L. (2007). Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov -w∞ *-Lie algebra.
Bouka, A; Accardi, L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/368
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