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Tau functions of the charged free bosons

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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 are given in the completion \(\widetilde{\cal M}\) by 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.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11531004) and the Simons Foundation (Grant No. 523868). The authors thank the anonymous referees whose comments have greatly improved this paper.

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Naihuan Jing & Zhijun Li

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

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  1. Naihuan Jing
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  2. Zhijun Li
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Correspondence to Zhijun Li.

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Jing, N., Li, Z. Tau functions of the charged free bosons. Sci. China Math. 63, 2157–2176 (2020). https://doi.org/10.1007/s11425-019-1735-4

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  • DOI: https://doi.org/10.1007/s11425-019-1735-4

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