Local Lorentz invariance and a new theory of gravitation equivalent to General Relativity

TL;DR

This paper develops a gauge theory of the Lorentz group with a novel emergent vierbein, establishing an equivalent formulation of gravity that aligns with General Relativity without higher derivatives.

Contribution

It introduces a Lorentz gauge theory with an emergent vierbein, providing a renormalizable, unitary alternative to traditional higher-derivative gravity theories.

Findings

The theory is equivalent to General Relativity when coupled to spin-zero matter.

The gauge field action is renormalizable and contains no higher derivatives.

The geometry is described by an $SO(1,3)$ Banach bundle.

Abstract

A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field, but emerges as a functional of the Lorentz gauge field. The underlying geometry of the theory turns out to be a $SO(1,3)$ Banach bundle. The most general action which is renormalizable by power-counting is constructed in terms of the gauge field and its first derivatives. It contains no higher derivative terms in the gauge field which destroy unitarity in the usual renormalizable $R^2$-theories of gravitation. Finally equivalence of the Lorentz gauge field theory coupled to spin zero matter with General Relativity is established