On Generalized WKB Expansion of Monodromy Generating Function
Mathematical Physics
2023-05-01 v2 High Energy Physics - Theory
Algebraic Geometry
math.MP
Symplectic Geometry
Abstract
We study symplectic properties of the monodromy map of the Schr\"odinger 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.
Keywords
Cite
@article{arxiv.2206.10578,
title = {On Generalized WKB Expansion of Monodromy Generating Function},
author = {Roman Klimov},
journal= {arXiv preprint arXiv:2206.10578},
year = {2023}
}