Time-dependent invariants for dirac equation and Newton–Wigner position operator

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For the Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of the 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 a particle with a kick modeled by a delta-function of time, the time-depending integral, which has the physical meaning of initial momentum, is found.