>>14383972>I'm having a hard time understanding this >What exactly does it mean?For every (differentiable) symmetry of a mechanical system (local if a field theory), there exists a conserved current (think: some conserved quantity). If your mechaincal system is, for example, a non-relativistic free point mass on infinite space, your system is invariant under spatial translations, which is a differentiable symmetry of your system. The associated conserved quantity then is just the momentum of the point mass. (As a little exercise: Would this still hold if the point mass is in a harmonic potential?)
