Quantum reduced loop gravity: extension to gauge vector field

TL;DR

This paper extends Quantum Reduced Loop Gravity to include gauge vector fields, quantizing their Hamiltonian and providing a foundation for analyzing quantum gravity effects on vector field dynamics.

Contribution

It introduces a method to quantize gauge vector fields within Quantum Reduced Loop Gravity, using regularization techniques similar to full Loop Quantum Gravity.

Findings

Regularization using Loop Quantum Gravity tools

Analytic matrix elements of the quantum operator

Foundation for quantum gravity corrections to vector fields

Abstract

Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements of the resulting operator between basis states are analytic coefficients. This analysis is the first step towards deriving the full quantum gravity corrections to the vector field semiclassical dynamics.