Say you have some arbitrary distribution of 4-current density and Faraday tensor in Minkowski space, which satisfies Maxwell's equations and the Lorentz force law. Has it ever been found worthwhile to Wick rotate such a problem to 4D Euclidean space in order to solve it, and if so, do any interesting features crop up upon doing so? Like, do charges behave in a qualitatively different manner in Euclidean space? I was wondering because I thought Wick rotation was only important for quantum theory, but then I saw the example here that shows it can be useful in classical physics too.
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