Effects of spacetime curvature on spin-1/2 particle zitterbewegung

Abstract

This paper investigates the properties of spin-1/2 particle zitterbewegung in the presence of a general curved spacetime background described in terms of Fermi normal coordinates, where the spatial part is expressed using general curvilinear coordinates. 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 spacetime curvature effects coupled to the zitterbewegung frequency. Also, the choice of curvilinear coordinates 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.