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Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model

Edwin Langmann
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Abstract

We present further remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers $N$ and $M$, and a particular function of $N+M$ variables arising as anyon correlation function of $N$ particles and $M$ anti-particles. In addition to identities obtained from anyons with the same statistics parameter $\lambda$, we also obtain ``dual'' relations involving ``mixed'' correlation functions of anyons with two different statistics parameters $\lambda$ and $1/\lambda$. We also give alternative, elementary proofs of these identities by direct computations.

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Edwin Langmann. 2004-06-24. Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model. https://doi.org/10.1063/1.2167807

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