Dirac-Kahler equations on curved spacetimes

TL;DR

This paper develops a Lagrangian framework for Dirac-Kahler equations on curved spacetimes, describing various fields with gauge and duality properties similar to the flat case, and analyzing their chiral components.

Contribution

It extends Dirac-Kahler equations to curved backgrounds using algebra-valued fields, revealing gauge and duality features in a geometric setting.

Findings

Fields include scalar, pseudo-scalar, vector, axial-vector, and field strength.

Chiral components are self-dual or anti-self-dual under Hodge duality.

The theory maintains gauge invariance and duality properties on curved spacetimes.

Abstract

A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type equation. Their components are scalar, pseudo-scalar, vector, axial-vector fields and fields strength which satisfy an irreducible systems of first-order Dirac-Kahler equations having remarkable gauge and duality properties similar to those of the flat case. The vector and axial-vector fields are the physical potentials giving rise to the field strength while the scalar fields play an auxiliary role and can be eliminated by fixing a suitable gauge. The chiral components of the field strength are either self-dual or anti self-dual with respect to the Hodge duality.