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A representation of \(\text{Spin}(4)\) on the eigenspinors of the Dirac operator on \(S^3\). (English) Zbl 0979.58012

The author constructs the eigenspinors of the Dirac operator \(D_3\) on the sphere \(S^3\) from a representation theoretical point of view. The corresponding eigenspaces give a highest weight representation of Spin(4). The eigenspinors are represented by using the matrix components of the irreducible representation of \(SU(2)\) and the actions of Spin(4) and \(D_3\) on the eigenspinors are calculated explicitly. It is possible to extend the results to zero mode spinors in \(D_4\) on \(S^4\).

MSC:

58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
81R25 Spinor and twistor methods applied to problems in quantum theory
81T20 Quantum field theory on curved space or space-time backgrounds
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