  A relativistic phase-space representation for a class of observables with
matrix-valued Weyl symbols proportional to the identity matrix
(charge-invariant observables)is proposed. We take into account the nontrivial
charge structure of the position and momentum operators. The evolution equation
coincides with its analog in relativistic quantum mechanics with nonlocal
Hamiltonian under conditions where particle-pair creation does not take place
(free particle and constant magnetic field). The differences in the equations
are connected with peculiarities of the constraints on the initial conditions.
An effective increase in coherence between eigenstates of the Hamiltonian is
found and possibilities of its experimental observation are discussed.
