Abstract
We describe the effect of a gauge transformation on the Chern–Simons functional in a thorough and unifying manner. We use the assumptions that the structure group is compact and connected and, in particular, that the principal bundle is flat. The Chern–Simons functional we consider is the one defined by choosing a flat reference connection. The most critical step in arriving at the main result is to show both the existence and the uniqueness of a cohomology class on the adjoint bundle such that it is the class of the so-called Maurer-Cartan 3 -form when restricted to each fiber.
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