Dirac equation on coordinate dependent noncommutative space-time

Abstract

We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on coordinate dependent noncommutative space-time (noncommutative Dirac equation) is proposed. The fundamental properties of this equation, like the Lorentz covariance and the continuity equation for the probability density are verified. To this end using the properties of the star product we derive the corresponding probability current density and prove its conservation. The energy-momentum tensor for the free noncommutative spinor field is calculated. We solve the free noncommutative Dirac equation and show that the standard energy-momentum dispersion relation remains valid in the noncommutative case.

Published version

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Cited by in corpus (8)

• Energy-dependent noncommutative quantum mechanics
• Noncommutative $R^d$ via closed star product
• Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane
• On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
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• Conserved symmetries in noncommutative quantum mechanics
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