Dirac operator on the Riemann sphere

Details Dirac operator on the Riemann sphere Dirac operator on the Riemann sphere

2002-12-11

arxiv.org/abs/hep-th/0212134v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, no figures, plain LaTeX

Scientific paper

We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |\lambda| - \half$. 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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