@ACuriousMind working on an answer and don't wan to to be an idiot, so I am making some general statements. please tell me if i am heading into a ditch. I was going to just post this first since I promised to post something Hi @cows
I am looking at [this][1] and [this][2]. Generally, for some solutions , for a given k. It seems one might need to read up on collective coordinates. We are thinking about the global gauge transformations g $\in$ G .
[1]: https://arxiv.org/pdf/hep-th/0509216.pdf