Split Extension of Internal Symmetry Group by the Poincaré Group

Abstract

The problem of combining internal symmetry and Lorentz invariance is thoroughly investigated for the case when the Poincare group is an invariant subgroup of a larger symmetry group. It is found that couplings are all minimal if the internal symmetry group does not have an abelian factor group. Possible couplings of this type are enumerated for the semi-simple internal symmetry group. A condition for releasing the coupling is also given, which is weakest among similar ones proposed so far in this direction. Physical implications of the result are not discussed.