On the choice of variable for quantization of conformal GR

TL;DR

This paper explores using spin connection components as variables for quantizing a conformal version of General Relativity, analyzing their properties and performing secondary quantization within a tetrad formalism.

Contribution

It introduces a novel approach by quantizing spin connection variables in a conformal GR model, maintaining classical correspondence while simplifying quantum interactions.

Findings

The model's gravitational action is quadratic in spin connections.

Quantum level analysis shows the model is trivial without self-interactions.

Classical correspondence to General Relativity is preserved.

Abstract

The possibility of using spin connection components as basic quantization variables of a conformal version of General Relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections in this model are analyzed. Secondary quantization of the chosen variables is performed. The gravitational part of the model action turns out to be quadratic with respect to the spin connections. So at the quantum level the model looks trivial, i.e., without quantum self-interactions. Meanwhile the correspondence to General Relativity is preserved at the classical level.