Conformal Invariance and the Metrication of the Fundamental Forces

TL;DR

This paper revisits Weyl's geometric approach to electromagnetism, proposing a modified framework that achieves metrication of all fundamental forces through conformal invariance and torsion, leading to a consistent quantum gravity theory in four dimensions.

Contribution

It introduces a novel geometric framework that unifies the metrication of all fundamental forces via conformal invariance and torsion, replacing Einstein gravity with conformal gravity.

Findings

Achieves metrication of electromagnetism using imaginary Weyl connection.

Extends the approach to Yang-Mills theories for all fundamental forces.

Proposes a consistent, unitary quantum conformal gravity in four dimensions.

Abstract

We revisit Weyl's metrication (geometrization) of electromagnetism. We show that by making Weyl's proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.