Torsion and Axial Current

TL;DR

This paper explores the influence of torsion and a scalar field on gravitation within Riemann-Cartan geometry, introducing a novel Lagrangian formalism that enables the construction of a conserved axial vector current independent of gauge choices.

Contribution

It proposes a new Lagrangian density derived from the SO(4,1) Pontryagin density, allowing conserved axial currents in complex geometries without relying on gauge fixing.

Findings

Conserved axial vector current can be constructed without gauge dependence.

The formalism links scalar fields to gauge connections in gravitation.

The approach applies to arbitrary background geometries.

Abstract

The role of torsion and a scalar field $\phi$ in gravitation, especially, in the presence of a Dirac field in the background of a particular class of the Riemann-Cartan geometry is considered here. Recently, a Lagrangian density with Lagrange multipliers has been proposed by the author which has been obtained by picking some particular terms from the SO(4,1) Pontryagin density, where the scalar field $\phi$ causes the de Sitter connection to have the proper dimension of a gauge field. In this formalism, conserved axial vector matter current can be constructed, irrespective of any gauge choice, in any manifold having arbitrary background geometry. This current is not a Noether current.