Instanton representation of Plebanski gravity XX. Minisuperspace quantization of gravity coupled to the Klein--Gordon scalar field

TL;DR

This paper develops a quantum framework for gravity coupled to a scalar field using the instanton representation, focusing on minisuperspace models and establishing a connection to semiclassical physics.

Contribution

It introduces a quantization scheme for gravity with a scalar field in minisuperspace, providing a well-defined Hilbert space and linking quantum results to classical limits.

Findings

Constructed a Hilbert space for the coupled system

Derived Hamilton's equations and verified consistency

Connected quantum states to semiclassical behavior

Abstract

In this paper we quantize the Klein--Gordon scalar field coupled to gravity in the instanton representation for spatially homogeneous variables. The construction provides a well-defined Hilbert space of states for generic self-interaction potential V, with a direct link to the semiclassical limit below the Planck scale. Additionally, we compute the Hamilton's equations of motion for this model, performing various consistency checks on the quantum theory.