Quantizing the line element field

TL;DR

This paper explores the classical and quantum properties of a vector field called the line element field, which can generate a metric with Lorentzian signature from a Euclidean metric, advancing understanding of quantum gravity models.

Contribution

It introduces and analyzes the classical and quantum aspects of the line element field, a novel approach to constructing Lorentzian metrics from Euclidean ones.

Findings

Classical properties of the line element field are characterized.

Quantum behavior of the line element field is studied.

Implications for quantum gravity are discussed.

Abstract

A metric with signature (-+++) can be constructed from a metric with signature (++++) and a double-sided vector field called the line element field. Some of the classical and quantum properties of this vector field are studied.