Influence of Gravity on noncommutative Dirac equation

TL;DR

This paper explores how gravity and noncommutativity affect the Dirac equation, showing that the equation's form remains consistent with modifications only in the covariant derivative, and applies this to particle creation in a cosmological setting.

Contribution

It demonstrates that the Dirac equation retains its form under gravity and noncommutativity, with a modified covariant derivative incorporating the noncommutative parameter, and applies this to particle creation analysis.

Findings

Modified covariant derivative depends on noncommutative parameter

Dirac equation form remains unchanged under gravity and noncommutativity

Computed particle density in anisotropic universe with electric field

Abstract

In this paper, we investigate the influence of gravity and noncommutativity on Dirac equation. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved space-time with an operator which depends on the noncommutative $\theta$-parameter. As an application, we have computed the density number of the created particles in presence of constant strong electric field in an anisotropic Bianchi universe.