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

作者: Jens Bolte , Stefan Keppeler

DOI: 10.1103/PHYSREVLETT.81.1987

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

参考文章(14)
Didier Robert, Autour de l'approximation semi-classique Birkhäuser. ,(1987)
V. Bargmann, Louis Michel, V. L. Telegdi, Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field Physical Review Letters. ,vol. 2, pp. 435- 436 ,(1959) , 10.1103/PHYSREVLETT.2.435
Robert G. Littlejohn, William G. Flynn, Geometric phases and the Bohr-Sommerfeld quantization of multicomponent wave fields. Physical Review Letters. ,vol. 66, pp. 2839- 2842 ,(1991) , 10.1103/PHYSREVLETT.66.2839
C. Emmrich, A. Weinstein, Geometry of the transport equation in multicomponent WKB approximations Communications in Mathematical Physics. ,vol. 176, pp. 701- 711 ,(1996) , 10.1007/BF02099256
Martin C. Gutzwiller, Jorge V. José, Chaos in classical and quantum mechanics ,(1990)
Barry Simon, Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase Physical Review Letters. ,vol. 51, pp. 2167- 2170 ,(1983) , 10.1103/PHYSREVLETT.51.2167
S. I. Rubinow, Joseph B. Keller, Asymptotic Solution of the Dirac Equation Physical Review. ,vol. 131, pp. 2789- 2796 ,(1963) , 10.1103/PHYSREV.131.2789
Michael Victor Berry, Quantal phase factors accompanying adiabatic changes Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 392, pp. 45- 57 ,(1984) , 10.1098/RSPA.1984.0023
L.H. Thomas, The Kinematics of an electron with an axis Philosophical Magazine Series 1. ,vol. 3, pp. 1- 21 ,(1927) , 10.1080/14786440108564170
Martin C. Gutzwiller, Chaos in Classical and Quantum Mechanics Interdisciplinary Applied Mathematics. ,(1990) , 10.1007/978-1-4612-0983-6