复化平面Kepler问题的单值性

Monodromy of complexified planar Kepler problem

受超对称量子场论和量子力学路径积分半经典分析的影响和天体力学中中心构型研究进展的启发,本文复化了经典的平面Kepler问题,并说明这是一个全纯的完全可积Hamilton系统.与传统的平面Kepler问题不同,本文进一步证明了这个全纯可积Hamilton系统存在非平凡的单值性,并提出了一个关于单值化群的猜想以及进一步的研究设想.

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 problem 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 problem.We also propose a conjecture about the whole monodromy group and some possible further directions including the physical implications of such nontrivial monodromies.