Conformal Gauge Relativity - On the Geometrical Unification of Gravitation and Gauge Fields

TL;DR

This paper proposes a geometric framework unifying gravitation and gauge fields within a Lagrangian formalism that extends General Relativity, providing a foundation for electromagnetism and matter stress-energy tensors.

Contribution

It introduces a geometric Lagrangian depending on metric, affine connection, and gauge generators, unifying gravity and gauge fields while maintaining compatibility with Einstein's theory.

Findings

Derives field equations from geometric invariance principles.

Provides a geometric foundation for the stress-energy tensor.

Unifies electromagnetism and gravity in a single geometric framework.

Abstract

A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along with Gravitation, at the time it gives a geometric foundation for the stress-energy tensor of continuous matter. The geometric-invariance principle under this integration is exposed and the resulting field equations are obtained. The theory is developed over the tangent space of a four-dimensional real manifold and the generators become those from the Homogenous Lorentz group.