arXiv subjects
Publications and source records attributed to Yoshihito Shimada.
In this paper, we consider Bogoliubov automorphisms of CAR algebra and we give implementers as continuous linear operators on the white noise (test or generalized) functionals for the Fermion system with the help of the Fock expansion.
In this paper, we give the white noise calculus for the Fermion system and prove the Fock expansion. Each continuous linear operator on Fermionic white noise functionals is uniquely represented by the series of integral kernel operators. This series is called the Fock expansion.
We consider the energy representation for the gauge group. The gauge group is the set of (C^{\infty})-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of (M). To prove irreducibility for the energy representation, we use the fact that each operator from the space of test functionals to the space of generalized functionals is realized as a series of integral kernel operators, called Fock expansion.
We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary representations of the infinite dimensional symplectic group are constructed via unitary implementors of Bogoliubov automorphisms. Complete classification of these representations up to quasi-equivalence is obtained.