The Phase-Space Noncommutativity Effect on the Large and Small Wavefunction Components Approach at Dirac Equation

TL;DR

This paper investigates how phase-space noncommutativity influences the nonrelativistic limit of the Dirac equation, connecting relativistic quantum mechanics with noncommutative geometry.

Contribution

It introduces a method to analyze the Dirac equation in noncommutative phase-space using wavefunction components, extending noncommutative effects to the nonrelativistic limit.

Findings

Noncommutativity modifies the Dirac equation's nonrelativistic limit.

The approach links relativistic and noncommutative quantum mechanics.

Potential implications for quantum systems in noncommutative spaces.

Abstract

By the large and small wave-function components approach we achieved the nonrela-tivistic limit of the Dirac equation in interaction with an electromagnetic potential in noncommutative phase-space, and we tested the effect of the phase-space noncommutativity on it, knowing that the nonrelativistic limit of the Dirac equation gives the Schr\"odinger-Pauli equation.