I recently discovered this paper :
Loop Representation of charged particles interacting with
Maxwell and Chern-Simons
fields (https://arxiv.org/pdf/hep-th/0107013v2.pdf) published in PRD in 2002.
where the authors are doing a field quantization of the Maxwell field with electric charges (so divE is not 0), and they obtain a solution with open paths (Faraday lines) which goes from the charge to infinity. This result is quite obvious, as it corresponds to the usual interpretation of faraday lines in classical fields.
This approach is interesting and different than the common way we defiene quantum field interactions, but this article doesn't look like popular (only few and self citations). Moreover, I didn't see other paper with the same approach (maybe I don't use the best keywords in my search). Is there a reason for that?
Richard Feynman gave lectures on this topic related to gravity that are collected into a book by his students. He had success in describing weak fields equivalent to GR with single loops that lead to renormalization. The effort failed when Feynman discovered that he needed multiple loops to describe strong fields and the path did not lead to renormalization. The persistence of infinities discredited the method.
The approach is different, but looks too cumbersome to be useful. Not even wrong.
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