The Rarita-Schwinger Operator on the 3-Sphere with Homogeneous Metric

16.01.2025, 16:15  –  Raum 0.14
Forschungsseminar Differentialgeometrie

Peter Grabs

We investigate the Rarita-Schwinger operator using methods previously applied in the Dirac case. The structure of the underlying manifold \(\mathcal{S}^3 \cong \mathrm{SU}(2)\) as a Lie group implies that all associated bundles are trivial, so their sections can be seen as ordinary functions.
Due to the compactness of \(\mathcal{S}^3\), the Peter-Weyl theorem provides a decomposition of such function spaces into finite-dimensional summands. This simplifies the analysis of the operator, reducing the problem to a finite-dimensional setting where eigenvalues can be computed using linear algebra techniques.