Lagrangian Formalism on Jet-Gauge and Jet-Diffeomorphism Groups: Towards a Unification of Gravity with Internal Gauge Interactions

TL;DR

This paper extends gauge theory formalism to include spacetime translations, unifying gravity with internal gauge interactions through jet-group structures and a central extension of the Poincare group.

Contribution

It introduces jet-gauge and jet-diffeomorphism groups and explores a novel unification approach of gravity with internal gauge fields via central extensions.

Findings

Reformulation of gauge theories with jet-bundles

Unification of gravity and electromagnetism through extended gauge symmetry

Framework for combining gravity with internal gauge interactions

Abstract

In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle formalism. We also reformulate these theories introducing the idea of jet-gauge and jet-diffeomorphism groups. Finally, we attempt to a simple, yet non-trivial, mixing of gravity and electromagnetism (or more general internal interaction) by turning to gauge symmetry a central extension of the Poincare group.