We provide an elegant homological construction of the extended phase space for linear Yang–Mills theory on an oriented and time-oriented Lorentzian manifold M with a time-like boundary $$\partial M$$ ∂ M that was proposed by Donnelly and Freidel (JHEP 1609:102, 2016). This explains and formalizes many of the rather ad hoc constructions for edge modes appearing in the theoretical physics literature. Our construction also applies to linear Chern–Simons theory, in which case we obtain the extended phase space introduced by Geiller (Nucl Phys B 924:312, 2017).

中文翻译：

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线性杨-米尔斯和陈-西蒙斯理论中边缘模式的同调视角

我们为线性 Yang-Mills 理论提供了一个优雅的扩展相空间的同调构造，该理论是由 Donnelly 和 Freidel 提出的，具有类似时间的边界 $$\partial M$$ ∂ M（ JHEP 1609:102, 2016)。这解释并形式化了出现在理论物理文献中的许多边缘模式相当特别的构造。我们的构造也适用于线性陈-西蒙斯理论，在这种情况下，我们获得了 Geiller 引入的扩展相空间（Nucl Phys B 924:312, 2017）。