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

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.