Dirac/Rarita-Schwinger plus Maxwell theories in $\mathbb{R} \times S^3$ spacetime in the Hopf coordinates

Abstract

We consider the sets of Dirac-Maxwell and Rarita-Schwinger-Maxwell equations in $\mathbb{R} \times S^3$ spacetime. Using the Hopf coordinates, we show that these equations allow separation of variables and obtain the corresponding analytic and numerical solutions. It is also demonstrated that the current of the Dirac field is related to the Hopf invariant on the $S^3 \rightarrow S^2$ fibration.