Quasi-classical trajectory-coherent approximation for the Dirac equation with an external electromagnetic field in Riemann-Cartan space. II. Construction of TCS and equation for spin

Abstract

For pt.I, see ibid., vol.8, p.515 (1991). Using Maslov's complex sprout method, special classes of the Ehrenfest-type approximate solutions of the Dirac equation in curved spacetime in the presence of external electromagnetic and torsion fields are constructed. They form a complete orthonormalized set of quasiclassical trajectory-coherent one-particle quantum states (TCS) and are strongly peaked around the worldline neighbourhood of the charged particle. The key tool in the TCS construction is the ' gamma -reconstruction' technique with the help of which it can be shown that the problem of TCS construction is reduced to the solution of the linear evolution equation for a two-component spinor. On the basis of the results obtained the generally covariant spinning equation of motion in the case of background gravitational, electromagnetic and torsion fields is deduced from the Dirac equation.