Instanton representation of Plebanski gravity XXII. Minisuperspace quantization of gravity coupled to spin 1/2 fermionic fields

TL;DR

This paper develops a quantum framework for gravity coupled with massless spin-1/2 fermions using the instanton representation of Plebanski gravity, constructing a Hilbert space and analyzing the classical-quantum correspondence.

Contribution

It introduces a novel quantization approach for gravity with fermions within the instanton Plebanski formalism, including Hilbert space construction and Hamiltonian analysis.

Findings

Classical equations are consistent with quantum dynamics.

Constructed a Hilbert space for the coupled gravity-fermion system.

Derived Hamilton's equations of motion for the model.

Abstract

In this paper we carry out a quantization of gravity coupled to massless spin 1/2 fermions through the instanton representation of Plebanski gravity. We have constructed a Hilbert space of states for this model, and we have computed the Hamilton's equations of motion. The classical equations appear, at a superficial level, to be consistent with the quantum dynamics of the theory.