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The minimal coupling principle is revisited under the quantum perspectives ofthe space-time symmetry. This revision is better realized on a Group Approachto Quantization (GAQ) where group cohomology and extensions of groups play apreponderant role. We firstly consider the case of the electromagneticpotential; the Galilei and/or Poincare group is (non-centrally) extended by the"local" U(1) group. This group can also be seen as a central extension,parametrized by both the mass and the electric charge, of aninfinite-dimensional group, on which GAQ leads to the dynamics of a particlemoving in the presence of an electromagnetic field. Then we try thegravitational interaction of a particle by turning into "local" the space-timetranslations. However, promoting to "local" the space-time subgroup of the truesymmetry of the quantum free relativistic particle, i.e. the centrally extendedby U(1) Poincare group, results in a new electromagnetic-like force of puregravitational origin. This is a consequence of the space-time translations notbeing an invariant subgroup of the extended Poincare group and constitutes apreliminary attempt to a non-trivial mixing of space-time and internal gaugeinteractions.Comment: 22 pages, LATEX, no figure

Gauge principle revisited: Towards a unification of space–time and internal gauge interactions