Semenov A. Phase Space Localization of a Scalar Charged Particle.

The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl—Wigner—Moyal formalism is proposed. The evolution equations are found to coincide with their counterparts in relativistic quantum mechanics with non-local Hamiltonian. The difference between the theories is connected with peculiarities of the constraints on the initial conditions. Effective increase in coherence between eigenstates of the Hamiltonian is found. Relativistic coherent states that take into account a non-trivial charge structure of the position and momentum operators and satisfy the charge superselection rule are considered. On this basis, the entangled coherent states are developed.