A Formula for Connected Bosonic \(n\)-Point Functions for the BKP Hierarchy

TL;DR

This paper derives a new formula for connected n-point functions of BKP hierarchy tau-functions by embedding into KP hierarchy, and proves its equivalence to a previous formula.

Contribution

It introduces a novel formula for BKP hierarchy connected n-point functions and demonstrates its equivalence to existing formulas, advancing the theoretical understanding.

Findings

Derived a new formula for BKP n-point functions

Proved the equivalence of the new formula with Wang and Yang's formula

Enhanced the theoretical framework for BKP hierarchy analysis

Abstract

We present a formula for the connected \(n\)-point functions of a tau-funtion of the BKP hierarchy by embedding BKP hierarchy into KP hierarchy. This formula is different from the one given by Wang and Yang. We prove that these two formulae are equivalent.