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

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.

preprint2009arXivOpen access
Geoffrey Lee
math-phmath.MP
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Geoffrey Lee

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