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 
different limits.