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Jens Bolte, Stefan Keppeler
A semiclassical approach to the Dirac equation
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ABSTRACT. We derive a semiclassical time evolution kernel and a trace formula for the
Dirac equation. The classical trajectories that enter the expressions are
determined by the dynamics of relativistic point particles. We carefully
investigate the transport of the spin degrees of freedom along the
trajectories which can be understood geometrically as parallel transport in a
vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in
terms of a classical spin vector that is transported along the trajectories
and whose dynamics, dictated by the equation of Thomas precession, gives rise
to dynamical and geometric phases every orbit is weighted by. We also
present an analogous approach to the Pauli equation which we analyse in two