Timeline for When is the action of the gauge group on the space of connections free?

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May 23, 2019 at 20:36	comment	added	mme		I edited the answer, partly to get away the technicalities of pinning down the trace theorems nicely or optimally, and partly because you already mentioned the possibility of such a decay condition on lines in your original post; the point of all the restriction stuff was to guarantee that the restriction to any line is $L^1$.
May 23, 2019 at 20:36	history	edited	mme	CC BY-SA 4.0	Sloppiness with $L^1$ spaces and trace theorems; I usually use $L^2$ so there come the wrong constants everywhere.
May 23, 2019 at 19:44	history	edited	mme	CC BY-SA 4.0	Sloppiness with $L^1$ spaces and trace theorems; I usually use $L^2$ so there come the wrong constants everywhere.
May 23, 2019 at 17:03	comment	added	mme		You of course need to impose a decay condition on the gauge transformations themselves, or the constant map $\sigma_g: \Bbb R^4 \to G$ at $g$ will be a gauge transformation which fixes the trivial connection, for all $g$.
May 23, 2019 at 17:02	history	edited	mme	CC BY-SA 4.0	added 15 characters in body
May 23, 2019 at 16:52	history	answered	mme	CC BY-SA 4.0