Revisited gauge principle: towards a unification of space-time and internal gauge interactions

TL;DR

This paper explores a group-theoretic approach to unifying space-time and internal gauge interactions, revealing new gravitational-like forces through group extensions and cohomology in quantum symmetry frameworks.

Contribution

It introduces a novel perspective on gauge unification using group cohomology and extensions, linking space-time and internal symmetries in quantum mechanics.

Findings

Extended Poincare group yields a gravitational-like force.

Local space-time translations lead to electromagnetic-like effects.

Group cohomology plays a key role in gauge interaction unification.

Abstract

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 firstly consider the case of the electromagnetic potential; 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 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 turning into "local" the space-time translations. 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 electromagnetic-like 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 non-trivial mixing of space-time and internal gauge interactions.