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arXiv · hep-th/0212134

Dirac operator on the Riemann sphere

A. A. Abrikosov Jr
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Abstract

We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $λ$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |λ| - \half$. They form on the sphere a complete orthonormal functional set alternative to conventional spherical spinors. The difference and relationship between the spherical spinors in question and the standard ones are explained.

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A. A. Abrikosov Jr. 2002-12-11. Dirac operator on the Riemann sphere. https://arxiv.org/abs/hep-th/0212134

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