I came across the following post regarding the boundary term in Chern-Simons theory (specifically the level quantization of the theory). I am new to differential forms so the following questions may be trivial, but either way:

  1. In equation (12) of the accepted answer, where did the self wedge product terms i.e. $F_{D}\wedge F_{D}$ go?

  2. Similarly, in (18), where did terms like $A_{S_{1}} \wedge dA_{S_{1}}$ go?

  3. What is the intuition behind the last statement: " the contributions from the adjacent parts of the different patches' boundaries cancel each other". How do I see this?

  • $\begingroup$ General tip: Avoid referring to the accepted answer as it may become unaccepted in the future. Instead use permalinks. $\endgroup$
    – Qmechanic
    Nov 24, 2023 at 9:27


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