On Generalized WKB Expansion of Monodromy Generating Function

Abstract

We study symplectic properties of the monodromy map of the Schrödinger equation on a Riemann surface with a meromorphic potential having second-order poles. At first, we discuss the conditions for the base projective connection, which induces its own set of Darboux homological coordinates, to imply the Goldman Poisson structure on the character variety. Using this result, we extend the paper [Theoret. and Math. Phys. 206 (2021), 258-295, arXiv:1910.07140], by performing generalized WKB expansion of the generating function of monodromy symplectomorphism (the Yang-Yang function) and computing its first three terms.

References in corpus (7)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities
• Darboux coordinates, Yang-Yang functional, and gauge theory
• The monodromy of meromorphic projective structures
• Hamiltonian structure of rational isomonodromic deformation systems
• Complex Chern--Simons bundles in the relative setting
• Periods of meromorphic quadratic differentials and Goldman bracket
• Variational formulas on spaces of SL(2) Hitchin's spectral covers