For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schrödinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton–Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found. 1
We extend a stochastic model underlying the Dirac equation in (1+1) dimensions to include the electromagnetic field. The mechanism which produces quantum behavior is the allowed Brownian motion in both time and space. The necessary complexification of the spinor field is achieved by allowing the movement of a particle from one sublattice in (1+1) dimensions to another orthogonal sublattice in a manner dictated by the external "electromagnetic" field. The Dirac equation is obtained without recourse to a formal analytic continuation in either the time variable or the probabilities involved.