Gravitational Field as a Generalized Gauge Field Revisited

TL;DR

This paper revisits a gauge theory formulation of gravity, emphasizing the role of the metric tensor as a gauge field and extending the framework to arbitrary n-dimensional spacetimes with extra dimensions.

Contribution

It provides a more complete formulation of gravity as a gauge theory of coordinate transformations applicable to any number of dimensions.

Findings

Extended gauge theory formulation valid for arbitrary dimensions

Clarified the role of the metric tensor as a gauge field

Highlighted the necessity of extra dimensions in the framework

Abstract

We add some comments to our old paper \cite{F-U} where the metric tensor was introduced as the gauge theory of general coordinate transformation. This formulation is more satisfactorily completed than the original one if it is required to be valid for arbitrary n dimensional spacetime. That is, our formulation asserts the presence of extra dimensions positively.