Extensions of automorphisms and gauge symmetries (Q1308455)

The authors characterize the automorphisms of a \(C^*\)-algebra \(\mathcal A\) which extend to automorphisms of the crossed product \(\mathcal B\) of \(\mathcal A\) by a compact group dual. They also treat the case where the inclusion \(\mathcal A\subset\mathcal B\) is equipped with a group of automorphisms commuting with the dual action. The results are used to draw certain conclusions on the structure of the degenerate vacua on the field algebra related to broken gauge symmetries in quantum field theory.