RENORMALIZED POWERS OF QUANTUM WHITE NOISE-Reference-Cited by-同舟云学术

RENORMALIZED POWERS OF QUANTUM WHITE NOISE

Published:2006-03 Issue:01 Volume:09 Page:129-147
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

ACCARDI LUIGI¹,BOUKAS ANDREAS²,FRANZ UWE³

Affiliation:

1. Centro Vito Volterra, Università di Roma Tor Vergata, Via Columbia, 2, 00133 Roma, Italy

2. Department of Mathematics and Natural Sciences, American College of Greece, Aghia Paraskevi, 15342 Athens, Greece

3. Département de Mathématiques de Besançon, Université de Franche-Comte, 16, route de Gray, 25030 Besançon Cedex, France

Abstract

We prove some no-go theorems on the existence of a Fock representation of the *-Lie algebra generated by [Formula: see text], where [Formula: see text], bs are the Hida white noise densities. In particular we prove the nonexistence of such a representation for any *-Lie algebra containing [Formula: see text]. This drastic difference with the quadratic case proves the necessity of investigating different renormalization rules for the case of higher powers of white noise.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025706002263

Reference9 articles.

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2. Renormalized Squares of White Noise¶and Other Non-Gaussian Noises as Lévy Processes¶on Real Lie Algebras

3. Quantum Theory and Its Stochastic Limit

4. L. Accardi and N. Obata, Publications of the Research Institute for Mathematical Sciences, Kyoto, RIMS Kokyuroku 957, ed. N. Obata (RIMS, 1996) pp. 1–15.

5. SECOND QUANTIZED AUTOMORPHISMS OF THE RENORMALIZED SQUARE OF WHITE NOISE (RSWN) ALGEBRA

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