Free Motion of a Dirac Particle with a Minimum Uncertainty in Position

TL;DR

This paper develops a covariant noncommutative algebra leading to a generalized uncertainty principle predicting a minimal length, and derives a modified Dirac equation and propagator for a free particle.

Contribution

It introduces a new covariant noncommutative algebra with deformation parameters and derives a generalized Dirac equation and propagator for free particles.

Findings

Predicts a minimal measurable length in space-time

Derives a generalized Dirac equation incorporating noncommutativity

Provides explicit solutions and a modified propagator for free Dirac particles

Abstract

In this paper, we present a covariant, relativistic noncommutative algebra which includes two small deformation parameters. Using this algebra, we obtain a generalized uncertainty principle which predicts a minimal observable length in measure of space-time distances. Then, we introduce a new representation for coordinate and momentum operators which leads to a generalized Dirac equation. The solutions of the generalized Dirac equation for a free particle will be explicitly obtained. We also obtain the modified fermionic propagator for a free Dirac particle.