Physical Review Letters · 1998 · 81 citations · 10 references
Natural SciencesPhysicsMathematical PhysicsQuantum MechanicsTheoretical PhysicsRelativistic ElectrodynamicsRelativistic MechanicsRelativistic PhysicsRelativistic Quantum MechanicsSpin DynamicsSpin-orbit CouplingCharged Particle OrbitsParticle Orbits In General RelativityQuantum PropagatorRelativistic Quantum DynamicsRelativistic Spin OperatorsSemiclassical AnalysisSpin Dynamics In RelativityThomas Precession
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.
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Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
Barry Simon · Physical Review Letters · 1983 · 1.9K citations