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

摘要

The minimal coupling principle is revisited under the quantum perspectives of the space-time symmetry. This revision is better realized on a group approach to quantization (GAQ) where group cohomology and extensions of groups play a preponderant role. We first consider the case of the electromagnetic potential; the Galilei and/or Poincare group is (noncentrally) extended by the "local" U(1) group. The resulting group can also be seen as a central extension, parametrized by both the mass and the electric charge, of an infinite-dimensional group, on which GAQ leads to the dynamics of a particle moving in the presence of an electromagnetic field. Then we try the gravitational interaction of a particle by making the space-time translations "local." However, promoting to "local" the space-time subgroup of the true symmetry of the quantum free relativistic particle, i.e., the centrally extended by U(1) Poincare group, results in a new electromagneticlike force of pure gravitational origin. This is a consequence of the space-time translations not being an invariant subgroup of the extended Poincare group and constitutes a preliminary attempt to a nontrivial mixing of space-time and internal gauge interactions. (C) 2003 American Institute of Physics. [References: 39]