Supersymmetric relativistic quantum mechanics in time-domain

A supersymmetric relativistic quantum theory in the temporal domain is developed for bi-spinor fields satisfying the Dirac equation. The simplest time-domain supersymmetric theory can be postulated for fields with time-dependent mass, showing an equivalence with the bosonic supersymmetric theory in time-domain. Solutions are presented and they are used to produce probability oscillations between mass states. As an application of this idea, we study the two-neutrino oscillation problem, showing that flavour state oscillations may emerge from the supersymmetry originated by the time-dependence of the unique mass of the neutrino. •A supersymmetric theory in a temporal domain can be consistently formulated for relativistic quantum particles.•This is a new idea that relies in the possible time-dependent mass of particles.•We apply this theory to the problem of two neutrino oscillations, using a time dependence of neutrino mass.•It is reproduced the well-known non-relativistic result for such oscillation, with correct numerical observational values.