Hi folks, could you give me some reference where a transition from the Minkowski Electrodynamics to the Euclidean one is done in every detail? Caveats, subtleties, etc. Thanks

I don't know if this helps ... but the general way of deriving classical from relativistic calculations is to assume v/c small and approximate to a low order using Taylor/binomial expansions.

Hi again dimetrio, I assume you're talking about the analytic continuation to imaginary time. As usual, it all depends on just how deep you want to go. If you want a truly rigorous full fledged mathematical discussion, you can consult the works of Glimm and Jaffe. A more friendly semi-rigorous discussion of the connection between Minkowski and Euclidean descriptions can be found in Schulman's path integral book. Tsvelik also spends a good deal of time in the early chapters of his book discussing the continuation to imaginary time and the relation between statistical mechanics and field theory. Almost all the field theory for physicists texts I can think of don't make much effort to be careful about such analytic continuations. The point is primarily to get the pole structure right and make handwaving about convergence a little less necessary. Unfortunately for the call to rigor, you can get the pole structure with "physical arguments," and physicists don't mind waving their hands! I'll take a look a look at my book shelf and see if I can find anything else.