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

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