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arXiv · 0903.1346

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

Dinesh Singh·Nader Mobed
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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.

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Dinesh Singh, Nader Mobed. 2009-08-27. Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung. https://doi.org/10.1088/0264-9381%2F26%2F18%2F185007

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