Compactification with $\pmb{U(1)}$ magnetic field within Dirac supersymmetry

Abstract

We consider Dirac-supersymmetric interactions, which produce CP-conserving separation of positive and negative energy solutions in the Dirac equation in order to investigate an alternative to the Kaluza-Klein mechanism. We review conditions under which separation is possible into free particle and compactified behaviors in different dimensions, with attention to spin degrees of freedom. We show a $U(1)$ constant magnetic field produces such kind of behavior; an explicit treatment is given to the 6-$d$ to 4-$d$ and 4-$d$ to 2-$d$ breaking cases and the spectrum is obtained. A dynamical mass-creation mechanism is suggested from the procedure.