arXiv 0909.00852009-09-06math-phmath.MP

The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann Sphere

Geoffrey Lee

备注：: 6 pages, 4 figures, typos fixed
发表信息：: J.Geom.Phys.61:172-179,2011
DOI：: 10.1016/j.geomphys.2010.09.023

英文摘要：

In this paper, we revisit the connection between the Riemann-Roch theorem and the zero energy solutions of the two-dimensional Dirac equation in the presence of a delta-function like magnetic field. Our main result is the resolution of a paradox - the fact that the Riemann-Roch theorem correctly predicts the number of zero energy solutions of the Dirac equation despite counting what seems to be the wrong type of functions.

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