Dirac's Contour Representation for Paraparticles

TL;DR

This paper extends Dirac's contour representation to paraparticle systems using deformed algebra techniques, providing an analytic framework where paraparticle operators act as deformed derivatives.

Contribution

It introduces a novel analytic representation for parabose and parafermi systems, linking operator actions to deformed differentiation that encodes paraparticle statistics.

Findings

Deformed algebra techniques successfully extend Dirac's contour representation.

Paraparticle annihilation operators correspond to deformed derivatives in the new representation.

In the parafermi case, the derivative's ket-domain consists of degree p polynomials.

Abstract

Dirac's contour representation is extended to parabose and parafermi systems by use of deformed algebra techniques. In this analytic representation the action of the paraparticle annihilation operator is equivalent to a deformed differentiation which encodes the statistics of the paraparticle. In the parafermi case, the derivative's ket-domain is degree $p$ polynomials.