Deformed Heisenberg algebra and fractional spin field in 2+1 dimensions

TL;DR

This paper constructs a minimal set of linear differential equations for relativistic fields with arbitrary fractional spin in 2+1 dimensions, utilizing a deformed Heisenberg algebra involving Klein operators.

Contribution

It introduces a novel approach using deformed Heisenberg algebra to describe fractional spin fields in lower-dimensional spacetime.

Findings

Derived minimal linear differential equations for fractional spin fields.

Established a link between deformation parameter and fractional spin value.

Provided a framework for studying fractional spin particles in 2+1 dimensions.

Abstract

With the help of the deformed Heisenberg algebra involving Klein operator, we construct the minimal set of linear differential equations for the (2+1)-dimensional relativistic field with arbitrary fractional spin, whose value is defined by the deformation parameter.