Fock space on ${\mathbb{C}}^{\infty }$ and Bose-Fock space

Abstract

In this paper, we introduce the Fock space over ${\mathbb{C}}^{\infty }$ and obtain an isomorphism between the Fock space over ${\mathbb{C}}^{\infty }$ and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in \cite{coburn1985}. As a physical application, we study the Gibbs state.