Generalized symmetries and Noether’s theorem in QFT

We show that generalized symmetries cannot be charged under a continuous global symmetry having Noether current. Further, only non-compact can symmetry. These results follow from finer classification of twist operators, which naturally extends to finite group symmetries. They unravel topological obstructions the strong version Noether's theorem in QFT, even if general conditions implemented locally by operators (weak version). use these rederive Weinberg-Witten's within local generalizing it massless particles arbitrary dimensions and representations Lorentz group. Several examples with twists but without currents are described. end up discussing for hold, dynamical aspects QFT's symmetries, scale vs conformal invariance connections Coleman-Mandula quantum gravity.