Gauge fields on Riemann-Cartan space-times

TL;DR

This paper explores gauge fields on Riemann-Cartan space-times using tensor-valued differential forms, revealing how torsion influences gauge interactions and imposing new restrictions on space-time structure.

Contribution

It demonstrates that minimal coupling in Riemann-Cartan space-times leads to gauge invariance with torsion interaction, differing from traditional action-based approaches.

Findings

Gauge invariance is maintained with torsion interaction.

Restrictions on non-Riemannian structure are derived.

Differences from traditional minimal coupling methods are analyzed.

Abstract

Gauge fields are described on an Riemann-Cartan space-time by means of tensor-valued differential forms and exterior calculus. It is shown that minimal coupling procedure leads to a gauge invariant theory where gauge fields interact with torsion, and that consistency conditions for the gauge fields impose restrictions in the non-Riemannian structure of space-time. The new results differ from the well established ones obtained by using minimal coupling procedure at the action formulation. The sources of these differences are pointed out and discussed.