Propagating torsion from first principles

TL;DR

This paper derives a propagating torsion model in Riemann-Cartan spacetimes from first principles, showing how torsion interacts with matter fields while preserving gauge symmetry.

Contribution

It introduces a new torsion model based on minimal action and coupling principles, with a scalar potential governing torsion and volume, and explores its interaction with matter fields.

Findings

Gauge fields can interact minimally with torsion without breaking gauge symmetry.

The torsion trace is derived from a scalar potential influencing spacetime volume.

The model's equations are formulated for vacuum and matter fields.

Abstract

A propagating torsion model is derived from the requirement of compatibility between minimal action principle and minimal coupling procedure in Riemann-Cartan spacetimes. In the proposed model, the trace of the torsion tensor is derived from a scalar potential that determines the volume element of the spacetime. The equations of the model are written down for the vacuum and for various types of matter fields. Some of their properties are discussed. In particular, we show that gauge fields can interact minimally with the torsion without the breaking of gauge symmetry.