Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung

TL;DR

This paper explores how space-time curvature influences the quantum jitter (Zitterbewegung) of spin-1/2 particles, revealing gravitational effects on quantum properties and potential violations of the weak equivalence principle.

Contribution

It introduces explicit formulas for gravitational contributions to Zitterbewegung in curved space-time, extending previous models to include general curvilinear coordinates and orbital motion.

Findings

Gravitational effects couple with Zitterbewegung frequency via Ricci curvature.

Space-time curvature induces non-inertial contributions to momentum evolution.

Zitterbewegung influences stability and propagation of particles in curved backgrounds.

Abstract

This paper investigates the properties of spin-1/2 particle Zitterbewegung in the presence of a general curved space-time background described in terms of Fermi normal co-ordinates, where the spatial part is expressed using general curvilinear co-ordinates. Adopting the approach first introduced by Barut and Bracken for Zitterbewegung in the local rest frame of the particle, it is shown that non-trivial gravitational contributions to the relative position and momentum operators appear due to the coupling of Zitterbewegung frequency terms with the Ricci curvature tensor in the Fermi frame, indicating a formal violation of the weak equivalence principle. Explicit expressions for these contributions are shown for the case of quasi-circular orbital motion of a spin-1/2 particle in a Vaidya background. Formal expressions also appear for the time-derivative of the Pauli-Lubanski vector due to space-time curvature effects coupled to the Zitterbewegung frequency. As well, the choice of curvilinear co-ordinates results in non-inertial contributions in the time evolution of the canonical momentum for the spin-1/2 particle, where Zitterbewegung effects lead to stability considerations for its propagation, based on the Floquet theory of differential equations.