>Look mom I picked a lagrangian which gave me the correct field theory after I already know the correct one!!111
Field theory, both classical and quantum, are fucking gay. Literally just sophistry with little physical or mathematical justification. Lagrangians this, action principle that, atleast for the lagrangian of a system of particles what is being done makes sense, but more often than not the lagrangians for fields are just given to you without explanation, and you're asked to minimize/maximize the action.