Canonical analysis of covariant unimodular gravity and an extension of the Kodama state

TL;DR

This paper performs a canonical and quantum analysis of covariant unimodular gravity, exploring the extension of the Kodama state and comparing quantum states across related theories.

Contribution

It provides a canonical formulation and quantization of covariant unimodular gravity and investigates the extension of the Kodama state within this framework.

Findings

Confirmed the extension of the Kodama state to covariant unimodular gravity

Compared quantum states of covariant unimodular gravity, original unimodular gravity, and general relativity

Clarified differences in quantum state structures among these theories

Abstract

We carry out the canonical analysis of a covariant version of unimodular gravity in terms of the connection representation. We then proceed to quantize this theory by implementing the Dirac procedure. We confirm whether and how the Kodama state, which is a solution of quantum general relativity, can be extended into covariant unimodular gravity. Finally, we discuss the difference of quantum states between covariant unimodular gravity, the original unimodular gravity, and general relativity.