R-deformed Heisenberg algebra, anyons and d=2+1 supersymmetry

TL;DR

This paper develops a universal framework using deformed Heisenberg algebra to describe anyons and spin fields in 2+1 dimensions, extending to supersymmetric systems and proposing a classical model for spin dynamics.

Contribution

It introduces a universal minimal spinor set of equations based on deformed Heisenberg algebra, generalized to supersymmetric systems, and explores classical models for spin in 2+1 dimensions.

Findings

Constructed universal differential equations for anyons and spins.

Extended the framework to supersymmetric field systems.

Proposed classical mechanical models for spin systems.

Abstract

A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d=2+1 supersymmetric field systems. Quadratic and linear forms of action functionals are found for the universal minimal as well as for supersymmetric spinor sets of equations. A possibility of constructing a universal classical mechanical model for d=2+1 spin systems is discussed.