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
2007-06-01
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.File | Dimensione | Formato | |
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07063397v2.pdf
accesso aperto
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235.79 kB
Formato
Adobe PDF
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235.79 kB | Adobe PDF | Visualizza/Apri |
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