Abstract
We present two ways to obtain precise expressions for the commuting Hamiltonians of the integrable system regarded as a fermionic limit of the quantum Calogero–Sutherland system as the number of particles tends to infinity with some special values of the coupling constant \(\beta\). The construction is realized in the Fock space.
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Acknowledgments
The author thanks S. M. Khoroshkin and A. K. Pogrebkov for the valuable remarks and fruitful discussions on the subject of the paper.
Funding
This research was supported by a grant from the Russian Science Foundation (Project No. 20-41-09009) and by the Simons Foundation.
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Appendix
It was proved in Proposition 2 that the densities \( \mathcal{W} _k(z)\) are linearly expressed in terms of \(w_n(z)\) given by (3.13). The first densities \(w_n(z)\) are given in Sec. 3.3. Here, we present the expressions for the first densities \( \mathcal{W} _k(z)\),
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Matushko, M.G. Calogero–Sutherland system at a free fermion point. Theor Math Phys 205, 1593–1610 (2020). https://doi.org/10.1134/S0040577920120041
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DOI: https://doi.org/10.1134/S0040577920120041