New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem

Details New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem

1996-07-28

arxiv.org/abs/hep-th/9607209v1

Physics

High Energy Physics

High Energy Physics - Theory

LATEX, 14 pages

Scientific paper

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a result two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated type Klein) surfaces are derived.

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