Tau functions of the charged free bosons

TL;DR

This paper investigates bosonic tau functions related to charged free bosons, proving the vacuum vector is the unique tau function in the Fock space and deriving new identities via boson-boson correspondence.

Contribution

It establishes the uniqueness of the tau function as the vacuum vector and introduces new q-series identities using bosonic methods.

Findings

The vacuum vector is the only tau function in the Fock space M.

Tau functions can be expressed using Schur functions.

New q-series identities are derived from boson-boson correspondence.

Abstract

We study bosonic tau functions in relation with the charged free bosonic fields. It is proved that up to a constant the only tau function in the Fock space M is the vacuum vector, and some tau functions were given in the completion of M using Schur functions. We also give a new proof of Borchardt's identity and obtain several q-series identities by using the boson-boson correspondence.