SL(2,C) Gauge Theory of Gravitation and the Quantization of the Gravitational Field

TL;DR

This paper proposes a novel approach to quantize gravity using SL(2,C) gauge theory, emphasizing the importance of manifold types near the big bang where classical metrics become inadequate.

Contribution

It introduces a new quantization framework for gravity based on SL(2,C) gauge theory applied to different types of manifolds, especially relevant near the big bang.

Findings

Quantization may be canonical within this framework.

Focus on manifolds where the metric loses meaning.

Potential for a new understanding of quantum gravity.

Abstract

A new approach to quantize the gravitational field is presented. It is based on the observation that the quantum character of matter becomes more significant as one gets closer to the big bang. As the metric loses its meaning, it makes sense to consider Schrodinger's three generic types of manifolds - unconnected differentiable, affinely connected, and metrically connected - as a temporal sequence following the big bang. Hence one should quantize the gravitational field on general differentiable manifolds or on affinely connected manifolds. The SL(2,C) gauge theory of gravitation is employed to explore this possibility. Within this framework, the quantization itself may well be canonical.