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

Dong Myung Chung, Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)533-559
Number of pages27
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Volume1
Issue number4
DOIs
Publication statusPublished - 1998 Oct
Externally publishedYes

ASJC Scopus subject areas

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

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