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arXiv · 1806.05037

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

C. Wiesendanger
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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

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C. Wiesendanger. 2018-06-09. Local Lorentz invariance and a new theory of gravitation equivalent to General Relativity. https://doi.org/10.1088/1361-6382%2Fab04e9

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