We construct the gauge-invariant electric and magnetic charges in Yang–Mills theory coupled to cosmological general relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser (Phys Lett B 116:259–263, 1982). For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

中文翻译：

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爱因斯坦-杨-米尔斯理论：规范不变电荷和线性化不稳定性

我们在与宇宙广义相对论（或任何其他几何引力）耦合的杨-米尔斯理论中构建规范不变的电荷和磁荷，扩展了 Abbott 和 Deser 的平坦时空结构（Phys Lett B 116:259-263, 1982）。对于非消失的背景规范场，电荷从重力部分获得了非平凡的贡献。此外，我们研究了对一阶微扰理论的约束，并建立了线性化不稳定性的条件：这就是一阶微扰理论的有效性。