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arXiv · 0909.0085

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

Geoffrey Lee
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Abstract

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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Geoffrey Lee. 2009-09-01. The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann Sphere. https://doi.org/10.1016/j.geomphys.2010.09.023

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