A brief survey of the renormalizability of four dimensional gravity for generalized Kodama states

TL;DR

This paper surveys the renormalizability of four-dimensional gravity using generalized Kodama states, exploring their quantum fluctuations, nonlinear transformations, and potential as a ground state in Ashtekar variables, aiming to address nonperturbative renormalizability.

Contribution

It introduces a framework for analyzing the renormalizability of gravity via generalized Kodama states and proposes a nonlinear transformation approach to understand their properties.

Findings

Examines quantum fluctuations around DeSitter spacetime.

Proposes the cubic tree network as a representation tool.

Lays groundwork for nonperturbative renormalizability analysis.

Abstract

We continue the line of research from previous works in assessing the suitability of the pure Kodama state both as a ground state for the generalized Kodama states, as well as characteristic of a good semiclassical limit of general relativity. We briefly introduce the quantum theory of fluctuations about DeSitter spacetime, which enables one to examine some perturbative aspects of the state. Additionally, we also motivate the concept of the cubic tree network, which enables one to view the generalized Kodama states in compact form as a nonlinear transformation of the pure Kodama states parametrized by the matter content of the proper classical limit. It is hoped that this work constitutes a first step in addressing the nonperturbative renormalizability of general relativity in Ashtekar variables. Remaining issues to address, including the analysis of specific matter models, include finiteness and normalizability of the generalized Kodama state as well as reality conditions on the Ashtekar variables, which we relegate to separate works.