Instanton representanton of Plebanski gravity. Gravitational coherent states

TL;DR

This paper constructs a Hilbert space of harmonic oscillator-like coherent states for Plebanski gravity's instanton representation, providing a new perspective and linking it to Ashtekar variables, with comparisons to loop quantum gravity.

Contribution

It introduces a novel coherent state formalism for Plebanski gravity's instanton representation and establishes a mapping to Ashtekar variables, enhancing the understanding of quantum gravity models.

Findings

Hilbert space of harmonic oscillator-like coherent states constructed

Invertible map between Ashtekar variables and the Hilbert space established

Comparison with loop quantum gravity results provided

Abstract

In this paper we show that the instanton representation of Plebanski gravity exhibits a Hilbert space of harmonic oscillator-like coherent states. We put in place the formalism and carry out the construction of the states, and we elucidate on their physical interpretation. Additionally, we provide an invertible map between the Ashtekar variables and this Hilbert space of states, via the instanton representation. Finally, we compare and constrast our formalism and some of our results with the corresponding ones in loop quantum gravity.