Loop quantization of a 3D Abelian BF model with sigma-model matter

TL;DR

This paper applies Loop Quantum Gravity techniques to a 3D Abelian BF model coupled with scalar fields, analyzing its symmetries, dynamics, and quantum structure, including the construction of the physical Hilbert space and observables.

Contribution

It develops a novel loop quantization framework for a 3D Abelian BF model with sigma-model matter, extending LQG methods to this coupled system.

Findings

Constructed the physical Hilbert space for the model

Identified key observables within the quantum theory

Analyzed the classical and quantum symmetries of the system

Abstract

The main goal of this work is to explore the symmetries and develop the dynamics associated to a 3D Abelian BF model coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. We apply to the present model the techniques of Loop Quantum Gravity, construct its physical Hilbert space and its observables.