Annihilation-derivative, creation-derivative and representation of quantum martingales

Un Cig Ji, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

On the basis of the quantum white noise theory we introduce the notion of creation- and annihilation-derivatives of Fock space operators and study the differentiability of white noise operators. We define the Hitsuda-Skorohod quantum stochastic integrals by the adjoint actions of quantum stochastic gradients and show explicit formulas for their creation- and annihilation-derivatives. As an application, we derive direct formulas for the integrands in the quantum stochastic integral representation of a regular quantum martingale.

Original languageEnglish
Pages (from-to)751-775
Number of pages25
JournalCommunications in Mathematical Physics
Volume286
Issue number2
DOIs
Publication statusPublished - 2009 Mar 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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