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I got curious on the limits of variatonal principle. As far as i know all of the theories can be reformulated as problem of finding extremum of some action. Not only that, but it seems to be most convenient method for looking for new theories in a lot of cases.

So my question is, what are the limits of it? Can any concievable theory be reformulated into variatonal problem with scalar lagrangian? Or the set of such theories is limited, and we are just lucky that so far nature seems to like this principle? Is there some good (mathematical) textbook dealing with this limits of variatonal principle?

Thanks:)