A Variation of Dirac Equation, Based on SO(2,1) Group, with Applications to Low Dimensional Systems

TL;DR

This paper introduces a modified Dirac equation based on the SO(2,1) group tailored for low-dimensional systems, developing non-unitary representations and quantum field theory applications for two-particle states.

Contribution

It presents a novel variation of the Dirac equation using SO(2,1) symmetry, specifically designed for low-dimensional physical systems.

Findings

Developed non-unitary representations for the SO(2,1) based Dirac equation

Formulated quantum field theory for the new relativistic equation

Applied the theory to low-dimensional two-particle systems like electron-hole pairs

Abstract

A variation of Dirac equation based on SO(2,1) group is suggested for treating low dimensional systems in the three dimensional x,y,t space. Non-unitary representations are developed in an analogous way to those used in the ordinary Dirac equations and quantum field theory is developed for the present SO(2,1) relativistic equation. The theory is applied for low dimensional systems including especially holes-electrons pairs, or other two-particle states, in the low dimensional space.