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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Symmetrien,Integrabilit
ät und Quantisierung

MP 2.3: Fachvortrag

Montag, 15. März 2004, 14:50–15:15, SR 2203

Semiclassical quantisation rules for the Dirac and Pauli equations — •Stefan Keppeler — Matematisk Fysik, LTH, Lunds Universitet, Box 118, 22100 Lund, Sweden

We derive explicit semiclassical quantisation conditions for the Dirac and Pauli equations [1,2]. We show that the spin degree of freedom yields a contribution which is of the same order of magnitude as the Maslov correction in Einstein-Brillouin-Keller quantisation. In order to obtain this result a generalisation of the notion of integrability for a certain skew product flow of classical translational dynamics and classical spin precession has to be derived. Among the examples discussed is the relativistic Kepler problem with Thomas precession, whose treatment sheds some light on the amazing success of Sommerfeld’s theory of fine structure [3].
[1] S. Keppeler, Phys. Rev. Lett. 89 (2002) 210405 and Ann. Phys. (NY) 304 (2003) 40-71
[2] S. Keppeler, Spinning Particles: Semiclassics and Spectral Statistics, Spinger Tracts in Modern Physics, vol. 193, Springer-Verlag Berlin Heidelberg, 2003
[3] A. Sommerfeld, Ann. Phys. (Leipzig) 51 (1916) 1-94 125-167