A rigged Hilbert space formalism is introduced to study Fock space operators. The symbols of continuous operators on a rigged Fock space are characterized in terms of Bargmann-Segal spaces and complex Gaussian integrals. In particular, characterizations of bounded operators and of operators of Hilbert-Schmidt class on the middle Fock space are obtained. As an application we establish an operator version of chaotic expansion (Wiener-Itô expansion) and describe a relation to the Fock expansion in terms of the Wick exponential of the number operator. As another application we discuss regularity property of a solution to a normal-ordered white noise differential equation generalizing a quantum stochastic differential equation.
Un Cig JI. Nobuaki OBATA. "A role of Bargmann-Segal spaces in characterization and expansion of operators on Fock space." J. Math. Soc. Japan 56 (2) 311 - 338, April, 2004. https://doi.org/10.2969/jmsj/1191418632