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arXiv · 2608.25297

Yang-Mills-Higgs-Schr\"odinger flow

Bo Chen·Chong Song
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Abstract

In this paper, we initiate the study of the Yang-Mills-Higgs-Schr\"odinger(YMHS) flow, i.e. the Hamiltonian flow of the Yang-Mills-Higgs functional defined on a symplectic fiber bundle. The YMHS flow provides a natural gauge-theoretic extension of the classical Schr\"odinger flow within the framework of symplectic reduction theory, and generalizes the Chern-Simons-Schr\"odinger equations to a non-Abelian gauge and non-linear fiber setting. We study its geometric structures and establish the local well-posedness of the corresponding Cauchy problem on compact Riemann surfaces.

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Bo Chen, Chong Song. 2026-08-26. Yang-Mills-Higgs-Schr\"odinger flow. https://arxiv.org/abs/2608.25297

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