An extended Dirac equation in noncommutative space-time

TL;DR

This paper develops an extended Dirac equation within a noncommutative space-time framework, revealing solutions with both massless and large mass states, and discusses their properties and interactions.

Contribution

It introduces a novel extended Dirac equation derived from a noncommutative space-time algebra, expanding the theoretical understanding of relativistic quantum mechanics.

Findings

The extended Dirac equation admits both massless and large mass solutions.

Coupling effects between the solutions are analyzed.

Implications for noncommutative geometry in quantum physics are discussed.

Abstract

Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed, as well as the effects of coupling the two solutions.