Axial Current and Noether Charge

TL;DR

This paper explores the connection between axial vector matter currents and Noether's theorem within a specialized Lagrangian formalism that emphasizes local Lorentz symmetries, revealing new insights into conserved quantities in gravitational theories.

Contribution

It demonstrates that conserved axial vector currents can be derived as a consequence of Noether's theorem in a formalism focusing on local Lorentz symmetries, extending previous results.

Findings

Axial currents are shown to be Noether conserved quantities.

The formalism reproduces results similar to Einstein-Hilbert gravity.

New links between torsion, axial currents, and symmetries are established.

Abstract

A decade ago, a Lagrangian density has been proposed by the author where only the local symmetries of the Lorentz subgroup of (A)ds group is retained. This formalism has been found to produce some results encompassing that of standard Einstein-Hilbert formalism. In the present article, the conserved axial vector matter currents, constructed in some earlier paper, have been found to be a result of Noether's theorem. PACS: 04.20.Fy, 04.20.Cv, 11.40.-q Keywords: Torsion, Axial Current, Noether's Theorem