Mixing internal and spacetime transformations: some examples and counterexamples

This paper addresses the question of whether in a gauge theory coupled to gravity, internal and spacetime transformations can be mixed. It is shown that if the VEV of the gauge field is flat, the symmetry group is always a product of internal and spacetime symmetries. On the other hand, if the VEV of the gauge field is not flat it is impossible to properly define the notion of 'spacetime' transformations; as a consequence, if the symmetry group is nontrivial, mixing generically occurs.