# BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions

```@article{Wang2022BKPHA,
title={BKP hierarchy, affine coordinates, and a formula for connected bosonic n-point functions},
author={Zhiyuan Wang and Chenglang Yang},
journal={Letters in Mathematical Physics},
year={2022}
}```
• Published 20 January 2022
• Mathematics
• Letters in Mathematical Physics
. We derive a formula for the connected n -point functions of a tau- function of the BKP hierarchy in terms of its aﬃne coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [46]. Moreover, we prove a simple relation between the KP-aﬃne coordinates of a tau-function τ ( t ) of the KdV hierarchy and the BKP-aﬃne coordinates of τ ( t / 2). As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Br…

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