Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system

TL;DR

This paper constructs an integrable model as a limit of the spin Calogero-Sutherland system with infinitely many fermionic particles, using fermionic Fock space and explicit formulas for Dunkl operators and Yangian generators.

Contribution

It introduces a new approach to analyze the fermionic limit of the spin Calogero-Sutherland model via projective limits and fermionic fields.

Findings

Explicit formulas for Dunkl operators in the fermionic limit

Construction of the integrable model in multicomponent fermionic Fock space

Connection between vertex operators and the fermionic limit of the system

Abstract

We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with $N$ fermionic particles, where $N$ tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit formulas for limits of Dunkl operators and the Yangian generators are presented by means of fermionic fields.