Reduction of gravity-matter and dS gravity to hypersurface

Abstract

The quantization scheme based on reduction of the physical states I. Y. Park, Hypersurface foliation approach to renormalization of ADM formulation of gravity, Eur. Phys. J. C 75(9) (2015) 459, arXiv:1404.5066 [hep-th] is extended to two gravity-matter systems and pure de Sitter (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.