Is Torsion a Fundamental Physical Field?

TL;DR

This paper explores the role of torsion as a fundamental physical field by analyzing the Lorentz connection in flat and curved space-time, linking it to matter and spinor fields.

Contribution

It introduces a framework connecting torsion to the Lorentz connection and spinor axial current, proposing torsion as a fundamental field in space-time geometry.

Findings

Torsion is identified with the Lorentz connection in flat space-time.

In curved space-time, torsion relates to matter and spinor axial currents.

The paper generalizes the Dirac and Yang-Mills equations to include torsion effects.

Abstract

The local Lorentz group is introduced in flat space-time, where the resulting Dirac and Yang-Mills equations are found, and then generalized to curved space-time: if matter is neglected, the Lorentz connection is identified with the contortion field, while, if matter is taken into account, both the Lorentz connection and the spinor axial current are illustrated to contribute to the torsion of space-time.