Effect of Noncommutativity of Space-time on Zitterbewegung

TL;DR

This paper investigates how noncommutative space-time, through $$-deformation and doubly special relativity, alters Zitterbewegung, providing first-order modifications and recovering standard results in the appropriate limits.

Contribution

It introduces first-order modifications to Zitterbewegung due to $$-deformation and DSR, extending the Dirac theory to noncommutative space-time frameworks.

Findings

First-order $$-deformation modifies Zitterbewegung.

Doubly special relativity approach alters Zitterbewegung.

Results recover standard Zitterbewegung as deformation parameters vanish.

Abstract

In this paper, we present the results of our investigation on the modification of Zitterbewegung due to the noncommutativity of the space-time. First, we study the effect of $\kappa$-deformation of the space-time on Zitterbewegung. For this, we start with the $\kappa$-deformed Dirac theory and using $\kappa$-deformed Dirac equation valid upto first order in deformation parameter $a$, we find the modification in the Zitterbewegung valid upto first order in the deformation parameter $a$. In the limit $a\rightarrow 0$, we get back the commutative result. Secondly, we find the modification in the Zitterbewegung due to the Magueijo-Smolin(MS) approach of doubly special relativity(DSR) and in the limit $E_p \rightarrow \infty$, we get back the result in the commutative space-time.