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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics