GENERALIZED WHITE NOISE OPERATOR FIELDS AND QUANTUM WHITE NOISE DERIVATIVES
Un Cig Ji, Nobuaki Obata · 2007
Regarding a Fock space operator as a function of quantum white noise = ( at;a t ; t2 T ), we introduce its quantum white noise derivatives (qwn- derivatives) as a kind of functional derivatives with respect to at and a t . We prove that every white noise operator is dierentiable and the qwn-derivatives form a gen- eralized white noise operator eld on T. We show a relation between qwn-derivatives and generalized quantum stochastic integrals. We obtain a condition under which qwn-derivatives are dened pointwisely.