Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

Abstract

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; γ^μ(x) are the covariant-fixed Dirac matrices; σ^α,β=(1/4)[γ^α, γ^β]: a(μ^bν)=(1/2) (a _μ b _ν +aνb _μ); [A, B]=A·B − B·A; A,B=A·B+B·A; g(x)=det(g _αβ(x));R ^α _αμν=∂_μΓ ^βν_βν −...; the speed of light c=1.