Gauge Group and Extensions of Poincaré Group

In order to unify in a single invariant group of the Quantum Electrodynamics the Poincare group and the gauge group, we study some type of topological extension of the Poincare group by the gauge group, seen as the additive group of an Hilbert space where is realized the representation of mass zero and spin zero of the Poincare group. It is shown that the semi-direct product is the only possible extension.