Fractional Supersymmetry

TL;DR

This paper introduces a novel form of symmetry called fractional supersymmetry, which generalizes traditional supersymmetry by involving Grassmannian-type coordinates that produce arbitrary phases upon exchange.

Contribution

It presents the concept of fractional supersymmetry, extending the symmetry framework to include non-standard phase relations between coordinates, with realization at the field theory level.

Findings

Defines fractional supersymmetry with arbitrary phase exchange

Realizes fractional supersymmetry within field theory

Extends traditional supersymmetry concepts

Abstract

A Symmetry between bosonic coordinates and some Grassmannian-type coordinates is presented. Commuting two of these Grassmannian-type variables results in an arbitrary phase (not just a minus sign). This symmetry is also realised at the level of the field theory.