Higher powers of quantum white noises in terms of integral kernel operators

Dong Myung Chung; Un Cig Ji; Nobuaki Obata

doi:10.1142/S0219025798000296

Higher powers of quantum white noises in terms of integral kernel operators

Dong Myung Chung, Un Cig Ji, Nobuaki Obata

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

A rigorous mathematical formulation of higher powers of quantum white noises is given on the basis of the most recent theory of white noise distributions due to Cochran, Kuo and Sengupta. The renormalized quantum Itô formula due to Accardi, Lu and Volovich is derived from the renormalized product formula based on integral kernel operators on white noise functions. During the discussion, the analytic characterization of operator symbols and the expansion theorem for a white noise operator in terms of integral kernel operators are established.

Original language	English
Pages (from-to)	533-559
Number of pages	27
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	1
Issue number	4
DOIs	https://doi.org/10.1142/S0219025798000296
Publication status	Published - 1998 Oct
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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