The Proca-field in Loop Quantum Gravity

TL;DR

This paper develops a non-perturbative, rigorous quantization of the Proca-field within Loop Quantum Gravity by introducing a scalar field, revealing new insights into the quantum role of the mass term.

Contribution

It applies Loop Quantum Gravity methods to the Proca-field, providing a novel, consistent quantization approach with a unique scalar field implementation.

Findings

Successful non-perturbative quantization of the Proca-field.

The mass term plays a different role in quantum theory than classically.

Introduction of a scalar field with distinct properties from spontaneous symmetry breaking.

Abstract

In this paper we investigate the Proca-field in the framework of Loop Quantum Gravity. It turns out that the methods developed there can be applied to the symplectically embedded Proca-field, giving a rigorous, consistent, non-perturbative quantization of the theory. This can be achieved by introducing a scalar field, which has completely different properties than the one used in spontaneous symmetry breaking. The analysis of the kernel of the Hamiltonian suggests that the mass term in the quantum theory has a different role than in the classical theory.