Generalized fermion algebra

TL;DR

This paper introduces a one-parameter generalized fermion algebra, explores its representations and coherent states, and discusses its physical relevance, especially in the context of the Calogero-Sutherland system.

Contribution

It presents a new generalized fermion algebra, studies its Fock and polynomial representations, and constructs associated coherent states, including the Grassmann-variable case.

Findings

Derived the Fock and polynomial representations of the algebra

Constructed fermionic coherent states labeled by Grassmann variables

Linked the algebra to the Calogero-Sutherland system

Abstract

A one-parameter generalized fermion algebra ${\cal B}_{\kappa}(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A special attention is devoted to the limiting case $\kappa \rightarrow 0$ where the fermionic coherent states, labeled by Grassmann variables, are obtained. The physical relevance of the algebra is illustrated throughout Calogero-Sutherland system.