Second quantization of the elliptic Calogero-Sutherland model

TL;DR

This paper constructs a quantum field theory model of anyons on a circle at finite temperature, providing a second quantization of the elliptic Calogero-Sutherland model and establishing a key identity for eigenfunction construction.

Contribution

It introduces a novel second quantization framework for the elliptic Calogero-Sutherland model using loop group techniques, enabling eigenfunction and eigenvalue analysis.

Findings

Derived an anyon Hamiltonian for second quantization

Proved a key identity for eigenfunction construction

Established a foundation for an eigenfunction algorithm

Abstract

We use loop group techniques to construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland Hamiltonian (this algorithm is elaborated elsewhere). This paper contains a detailed introduction, technical details and proofs.