A representation of \(\text{Spin}(4)\) on the eigenspinors of the Dirac operator on \(S^3\) (Q5930115)
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scientific article; zbMATH DE number 1587439
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A representation of \(\text{Spin}(4)\) on the eigenspinors of the Dirac operator on \(S^3\) |
scientific article; zbMATH DE number 1587439 |
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A representation of \(\text{Spin}(4)\) on the eigenspinors of the Dirac operator on \(S^3\) (English)
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1 February 2002
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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 \(S^4\).
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Dirac operator
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eigenspinors
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irreducible decomposition
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representation theory
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