I just wanted to know what the characteristic property of a Lagrangian is?
How do you see without referring to Newtonian Mechanics that it has to be $L=T-V$?
People constructed a Lagrangian in Special Relativity and General Relativity. But is there a general recipe to find a Lagrangian for a theory or is a Lagrangian just chosen so that it works out?
Of course there are some symmetry and invariance properties that play an important role there, but is it possible to put the theory of Lagrangian to a more abstract and general level so that we can say a priori how a Lagrangian for a given theory must look like?
Which information are necessary to construct a Lagrangian for a physical theory?