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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Langmann, Edwin
Format: Preprint
Published: 2004
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916589200211968
author Langmann, Edwin
author_facet Langmann, Edwin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_math_ph_0406061
institution arXiv
publishDate 2004
record_format arxiv
spellingShingle Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
Langmann, Edwin
Mathematical Physics
High Energy Physics - Theory
Exactly Solvable and Integrable Systems
35Q58, 81T40
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.
title Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
topic Mathematical Physics
High Energy Physics - Theory
Exactly Solvable and Integrable Systems
35Q58, 81T40
url https://arxiv.org/abs/math-ph/0406061