Telling compositeness at a distance with outer automorphisms and CP

Abstract We investigate charge-parity (CP) and non-CP outer automorphisms of groups the transformation behavior group representations under them. identify situations where composite elementary states that transform in exactly same representation group, differently automorphisms. This can be instrumental discriminating from solely by their quantum numbers with respect to automorphism, i.e. without need for explicit short distance scattering experiments. discuss what conditions such a distinction is unequivocally possible. cleanly separate case symmetry constrained (representation) spaces multiple copies identical flavor space, which non-trivial space enforced states. Next product states, we also non-product representations. Comprehensive examples are given based on finite Σ(72) D8. The discussion applies SU(N) scrutinize recent claims literature SU(2N) antisymmetric matrices correspond distinct show automorphism transformations related an inner standard Z2 SU(N).
As direct implication, no arise SU(N).