Supersymmetric relativistic quantum mechanics in time-domain

TL;DR

This paper develops a supersymmetric relativistic quantum theory in the time domain for bi-spinor fields, demonstrating its application to neutrino oscillations and revealing new insights into mass state probability oscillations.

Contribution

It introduces a novel time-domain supersymmetric framework for relativistic quantum fields, linking it to neutrino flavor oscillations and mass dynamics.

Findings

Time-dependent mass fields exhibit supersymmetry in the time domain.

Probability oscillations between mass states are demonstrated.

Application to neutrino oscillations shows supersymmetry can explain flavor changes.

Abstract

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.