Dirac-like Affine Fields in 3D

TL;DR

This paper generalizes the Dirac equation to three-dimensional Minkowski space with extended symmetry groups, proposing new equations and constraints to interpret particle states.

Contribution

It introduces Dirac-like equations based on $ar{SL}(3,R)$ representations, expanding the mathematical framework for particle descriptions in 3D.

Findings

Formulation of Dirac-like equations with $ar{SL}(3,R)$ symmetry.

Constraints for physical interpretation of particle states.

Outline of equations for both multiplicity-free and infinite-component representations.

Abstract

A generalization of the Dirac field equation in three-dimensional Minkowski space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$ symmetry is considered. Constraints that ensure a correct physical interpretation of the corresponding particle states are presented. Dirac-like equations based on both multiplicity-free and generic infinite-component $\bar{SL}(3,R)$ representations are outlined.