1996/07/28 by N. V. Borisov, Borisov, N. V., Kirill Ilinski +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #funct-an #gr-qc #hep-th #math.FA
paper · pdf · doi:10.48550/arxiv.hep-th/9607209
LATEX, 14 pages
arxiv created 1996/07/28 · openalex publication_date 1996/07/28 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.