On the Zitterbewegung Transient Regime in a Coarse-Grained Space-Time

TL;DR

This paper investigates how a fractional Dirac equation in a coarse-grained medium causes Zitterbewegung to become a transient oscillation, explaining observational difficulties and supporting particle substructure theories.

Contribution

It introduces a fractional version of Dirac's equation showing Zitterbewegung as a transient phenomenon in a coarse-grained medium, unlike the purely oscillatory behavior in the standard case.

Findings

Zitterbewegung exhibits transient oscillations in fractional media.

Complex interactions dampen the Zitterbewegung motion.

Supports particle substructure hypotheses in quantum mechanics.

Abstract

In the present contribution, by studying a fractional version of Dirac's equation for the electron, we show that the phenomenon of Zitterbewegung in a coarse-grained medium exhibits a transient oscillatory behavior, rather than a purely oscillatory regime, as it occurs in the integer case, $\alpha=1$. Our result suggests that, in such systems, the Zitterbewegung-type term related to a trembling motion of a quasiparticle is tamed by its complex interactions with other particles and the medium. This can justify the difficulties in the observation of this interesting phenomenon. The possibility that the Zitterbewegung be accompanied by a damping factor supports the viewpoint of particle substructures in Quantum Mechanics.