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I sort of understand the mathematical content of the theorem, that

But what I don't understand is, intuitively, what sort of possibilities are ruled out. I've heard it said that flavor conservation laws such as conservation of lepton number and baryon number cannot be exact. Even if there are no single Feynman diagrams that show a violation of conservation of such quantities, they are not expected to hold in non-perturbative field theory. There's also the "no-hair" claim about black holes--black holes have definite charges and angular momentum and so-forth, but don't conserve anything else such as baryon number. Are these all related issues involving non-conservation?[Any reasonable theory with a mass gap] can only have a Lie group symmetry which is always a direct product of the Poincaré group and an internal group.