Abstract
Motivated by semi-classical analysis of path integrals in supersymmetric quantum field theory and quantum mechanics and inspired by the recent progress on central configurations in celestial mechanics, we complexify the classical planar Kepler 问题 which is a holomorphic completely integrable Hamiltonian system. The novelty is that this holomorphic integrable Hamiltonian system has nontrivial monodromy, which is different from the traditional planar Kepler 问题. We also propose a 猜想 about the whole monodromy group and some possible further directions including the physical implications of such nontrivial monodromies.
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