Macroscopic and Microscopic Paradigms for the Torsion Field: from the Test-Particle Motion to a Lorentz Gauge Theory

TL;DR

This paper compares macroscopic and microscopic paradigms for propagating torsion fields, examining their theoretical foundations and implications for particle motion and matter coupling in extensions of General Relativity.

Contribution

It introduces and analyzes two distinct paradigms for propagating torsion: a macroscopic potential-based approach and a microscopic gauge-theoretic approach.

Findings

Macroscopic approach clarifies test-particle trajectories influenced by torsion.

Microscopic approach reveals torsion coupling with matter's spin momentum.

Both paradigms offer complementary insights into torsion dynamics.

Abstract

Torsion represents the most natural extension of General Relativity and it attracted interest over the years in view of its link with fundamental properties of particle motion. The bulk of the approaches concerning the torsion dynamics focus their attention on their geometrical nature and they are naturally led to formulate a non-propagating theory. Here we review two different paradigms to describe the role of the torsion field, as far as a propagating feature of the resulting dynamics is concerned. However, these two proposals deal with different pictures, i.e., a macroscopic approach, based on the construction of suitable potentials for the torsion field, and a microscopic approach, which relies on the identification of torsion with the gauge field associated with the local Lorentz symmetry. We analyze in some detail both points of view and their implications on the coupling between torsion and matter will be investigated. In particular, in the macroscopic case, we analyze the test-particle motion to fix the physical trajectory, while, in the microscopic approach, a natural coupling between torsion and the spin momentum of matter fields arises.