Multitime quantum theory

A system of linearly independent, orthogonal solutions for the Dirac equation is found in a space with a three-dimensional time vector. The interaction with an electromagnetic field and the transition to the nonrelativistic limit are considered. In contrast to the customary one-time Dirac equation the wave function norm has alternating signs (ψ bar ψ = ±1), and the Hamiltonian describing the interaction with the electromagnetic field is a non-Hermitian operator. The latter is stipulated by a time dependence of the energy vector components which takes place even in the case of a constant modulus of the energy. Rules of the quantization of the spinor and the electromagnetic fields preserving the positive definiteness of the energy are defined