  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.
