Reduction of gravity-matter and dS gravity to hypersurface

TL;DR

This paper extends a state reduction quantization scheme to gravity-matter systems and de Sitter gravity, highlighting renormalizability, absence of infrared divergence, and the importance of the lapse function constraint.

Contribution

It introduces a novel quantization approach for gravity-matter and de Sitter gravity, emphasizing gauge-fixing and the role of the lapse function constraint.

Findings

Renormalizability established in flat background

Infrared divergence does not occur in this scheme

Lapse function constraint is crucial for quantization

Abstract

The quantization scheme based on reduction of the physical states \cite{Park:2014tia} is extended to two gravity-matter systems and pure dS gravity. For the gravity-matter systems we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role.