# Is there a systematic way to obtain all conserved quantities of a system?

I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's equations. These equations are invariant under many transformations (Lorentz transformation, rotations, spatial and temporal translations, etc. By the way is there a way, maybe from group theory, to find all the possible transformations that leaves the equation(s) invariant?) which imply as many conserved quantities thanks to Noether's theorem. In wikipedia I can see an equation that seems to give all the conserved quantities (wiki's article) but it involves the Lagrangian and I'm not sure whether the formula is valid for all systems whose Lagrangian is possible to obtain.

• See my post physics.stackexchange.com/q/296555 – iiqof Dec 5 '16 at 9:27
• @AngelJoaniquetTukiainen could you please comment on Ted Pudlik's answer below then? If I understand well, there exist a systematic way to obtain all conserved quantities of a system but it might involve tedious PDE systems to solve? And this is valid provided we do find the Lagrangian of the system. – thermomagnetic condensed boson Dec 5 '16 at 20:15
• I don't understand the request, what do you want me to coment? And yes, you have understand it correctly. – iiqof Dec 5 '16 at 20:56
• @AngelJoaniquetTukianen Ted Pudlik claimed that there is no general algorithm to obtain the conserved quantities of a system while you claim that there is, under certain circumstances. I think it'd be nice if there some discussion with Ted occur. – thermomagnetic condensed boson Dec 5 '16 at 21:43