The identification of the *-Lie algebra of the renormalized higher powers of White noise (RHPWN) and the analytic continuation of the second quantized centreless Virasoro (or Witt)-Zamolodchikov-omega(infinity)*-Lie algebra of conformal field theory and high-energy physics, was recently established in [5] based on results obtained in [3] and [4]. In the present paper, we show how the RHPWN Fock kernels must be truncated in order to be positive semi-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.
Accardi, L., Boukas, A. (2008). Fock representation of the renormalized higher powers of White noise and the centreless Virasoro (or Witt)-Zamolodchikov-omega(infinity)*-Lie algebra. In Journal of Physics A: Mathematical and theoretical. BRISTOL : IOP Publishing [10.1088/1751-8113/41/30/304001].
Fock representation of the renormalized higher powers of White noise and the centreless Virasoro (or Witt)-Zamolodchikov-omega(infinity)*-Lie algebra
ACCARDI, LUIGI;
2008-01-01
Abstract
The identification of the *-Lie algebra of the renormalized higher powers of White noise (RHPWN) and the analytic continuation of the second quantized centreless Virasoro (or Witt)-Zamolodchikov-omega(infinity)*-Lie algebra of conformal field theory and high-energy physics, was recently established in [5] based on results obtained in [3] and [4]. In the present paper, we show how the RHPWN Fock kernels must be truncated in order to be positive semi-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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