Fermionic limit of the Calogero-Sutherland system

TL;DR

This paper constructs an integrable model as a limit of Calogero-Sutherland systems with many fermionic particles, providing explicit formulas for operators and Hamiltonians using vertex operators.

Contribution

It introduces a novel projective limit approach to Calogero-Sutherland models, extending their analysis to infinite particle systems with explicit operator formulas.

Findings

Explicit formulas for Dunkl operator limits

Construction of an integrable infinite-particle model

Application of vertex operators to limit processes

Abstract

We present a construction of an integrable model as a projective type limit of Calogero-Sutherland models of $N$ fermionic particles, when $N$ tends to infinity. Explicit formulas for limits of Dunkl operators and of commuting Hamiltonians by means of vertex operators are given.