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Integrability of Liouville System on High Genus Riemann Surface. I. Classical Case

Y Chen

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Abstract

By using the theory of uniformization of Riemann surfaces, we study properties of the Liou- ville equation and its general solution on a Riemann surface of genus g1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface.

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What this paper is about

By using the theory of uniformization of Riemann surfaces, we study properties of the Liou- ville equation and its general solution on a Riemann surface of genus g1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface.

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Available abstract

By using the theory of uniformization of Riemann surfaces, we study properties of the Liou- ville equation and its general solution on a Riemann surface of genus g1. After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices, we prove the classical integrability of Liouville system on high genus Riemann surface.

Key concepts: Riemann surface, Uniformization theorem, Genus, Formalism (music), Uniformization (probability theory), Geometric function theory, Riemann's differential equation, Riemann problem

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