Canonical quantization of Plebanski gravity in diagonal variables

TL;DR

This paper transforms Ashtekar's formulation of General Relativity into a reduced, explicit degrees of freedom theory, performs canonical analysis, quantizes it, and clarifies its canonical structure relative to the original formulation.

Contribution

It introduces a reduced canonical framework for Plebanski gravity, enabling explicit degrees of freedom and a new quantization approach.

Findings

Constructed a Hilbert space of states for zero cosmological constant.

Performed classical dynamics analysis in the reduced theory.

Clarified the canonical structure of the dual theory.

Abstract

In this paper we have carried out a transformation from Ashtekar's theory of GR into a reduced theory where the physical degrees of freedom are explicit. We have performed the canonical analysis, computed the classical dynamics and have performed a quantization on this reduced space, constructing a Hilbert space of states for vanishing cosmological constant. Finally, we have clarified the canonical structure of the dual theory in relation to the original Ashtekar theory.