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MP: Theoretische und Mathematische Grundlagen der Physik

MP 3: Hauptvortr
äge III

MP 3.2: Hauptvortrag

Donnerstag, 18. März 1999, 11:05–11:55, MA1

Semiclassical time evolution of Dirac spinors — •Jens Bolte — Abteilung Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm

An application of the WKB-method to the Dirac equation for an electron in external electromagnetic fields allows for a separation of the translational and the spin degrees of freedom. To leading semiclassical order the spin dynamics is dictated by a transport equation that has to be solved along the classical trajectories of the translational degrees of freedom. The solutions of the transport equation can be viewed as semiclassical time evolution operators for the spin degrees of freedom. Geometrically, the spin transport can be understood as parallel transport in the eigenvector bundle of the symbol matrix of the Dirac Hamiltonian. An interpretation in terms of a classical spin precessing along particle trajectories is provided and the occurence of geometric phases is discussed. A knowledge of the semiclassical spin transport turns out to be necessary for a semiclassical representation of the time evolution kernel for the Dirac equation in terms of classical quantities. Finally, a semiclassical trace formula can be derived.