Can every physically sound differential equation, that is covariant, deterministic etc. be derived by extremising a suitable action using a suitable lagrangian, that may be arbitary. Is this a mathematical theorem?
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/20298/2451 , physics.stackexchange.com/q/20188/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Oct 20, 2014 at 18:35
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$\begingroup$ Short answer, yes, almost all physical equations (even Shrodiger and Dirac euqations) can be fomrulated as action extremum principles. Several textbooks actualy provide the action form of the equations a swell. Mathematicaly, it is relatively easy to transform any set of equations into a functional integral (or functional equation) similar to action principle $\endgroup$– Nikos M.Commented Oct 20, 2014 at 19:22
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$\begingroup$ Just because an equation derives from an action or a Lagrangian does not make it "physically sound". Most physicists actually believe that there is only one physical equation (TOE) and that all other equations are merely approximations for special cases. $\endgroup$– CuriousOneCommented Oct 20, 2014 at 20:09
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