Dirac eigenspinors on a three-sphere

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 where is the radius.  This paper contains an analysis that seems applicable:  HommaSpin4RepDiracEigenspinorsS3

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