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arXiv · 2607.06246

A Note on the Rainich Problem for SU(2) Gauge

Hanwen Liu
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Abstract

We provide a resolution to the non-Abelian Rainich problem. By canonically identifying traceless symmetric $(0,2)$-tensors with Hermitian forms on the vector bundle of chiral 2-forms, we define the internal square roots of a stress-energy tensor. We then prove that the existence of a local $\operatorname{SU}(2)$ Yang-Mills field with prescribed stress-energy tensor $T$ is equivalent to a single differential condition on internal square roots of $T$.

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Hanwen Liu. 2026-07-07. A Note on the Rainich Problem for SU(2) Gauge. https://arxiv.org/abs/2607.06246

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