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The question of the relation between eigenspinors of Dirac operator on a compact manifold — I only care about S4 in the end — and photons animates my study.  We know from the work of Christian Bar and other that the spectrum is exactly integer multiples of $1/R$ where $R$ is the radius.  This paper contains an analysis that seems applicable:  HommaSpin4RepDiracEigenspinorsS3