On Anyonic Propagators

TL;DR

This paper develops a path integral framework for fractional spin particles, deriving propagators in electromagnetic fields with flexible boundary conditions, advancing theoretical understanding of anyonic behavior.

Contribution

It introduces a novel path integral representation for anyonic propagators that simplifies calculations by removing constraints and accommodating arbitrary boundary conditions.

Findings

Derived a propagator for fractional spin particles in electromagnetic fields.

Established a path integral approach that handles arbitrary boundary conditions.

Simplified the representation by eliminating time derivatives after bosonic integration.

Abstract

We consider a simple action for a fractional spin particle and a path integral representation for the propagator is obtained in a gauge such that the constraint embodied in the Lagrangian is not an obstacle. We obtain a propagator for the particle in a constant electromagnetic field via the path integral representation over velocities, which is characterized by arbitrary boundary conditions and the absence of time derivatives following integration over bosonic variables.