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arXiv:quant-ph/9805041 · Physical Review Letters

Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles

Jens Bolte, Stefan Keppeler

Published Sep 7, 1998• 81 citations
arXivHTMLPDF

Abstract

We investigate the Dirac equation in the semiclassical limit $\ensuremath{\Elzxh}\ensuremath{\rightarrow}0$. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.

DOI
10.1103/physrevlett.81.1987

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We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate-space formulation. Using a coherent-state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum-mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.
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Abstract We derive semiclassical trace formulae including Gutzwiller's trace formula using coherent states. This formulation has several advantages over the usual coordinate‐space formulation. Using a coherent‐state basis makes it immediately obvious that classical periodic orbits make separate contributions to the trace of the quantum‐mechanical time evolution operator. In addition, our approach is manifestly canonically invariant at all stages, and leads to the simplest possible derivation of Gutzwiller's formula.
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