Addendum to: Second quantization of the elliptic Calogero-Sutherland model

Edwin Langmann A

Published Jun 24, 2004• 0 citations

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 λ, we also obtain “dual ” relations involving “mixed” correlation functions of anyons with two different statistics parameters λ and 1/λ. We also give alternative, elementary proofs of these identities by direct computations.

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