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

TL;DR

This paper introduces a new Fock space over infinite-dimensional complex space, establishes an isomorphism with Bose-Fock space, and explores operator representations and physical applications like Gibbs states.

Contribution

It presents the first isomorphism between Fock space over ^ and Bose-Fock space, enabling new operator representations and physical insights.

Findings

Established an isomorphism between Fock and Bose-Fock spaces

Derived new operator representations on Bose-Fock space

Analyzed Gibbs state in the context of the new framework

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.