Local Lorentz invariance and a new theory of gravitation equivalent to General Relativity
arXiv:1806.05037 · doi:10.1088/1361-6382/ab04e9
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 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 -theories of gravitation. Finally equivalence of the Lorentz gauge field theory coupled to spin zero matter with General Relativity is established
25 pages