Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation

TL;DR

This paper introduces a new Lorentz covariant helicity tensor in Maxwell theory, unifying various conservation laws related to light's helicity, spin, and infra-zilch, and deriving it as a Noether current from a duality-symmetric Lagrangian.

Contribution

It presents the first Lorentz covariant formulation of the helicity hierarchy in Maxwell theory using a novel conserved tensor.

Findings

The helicity tensor is Lorentz covariant and conserved.

It arises as a Noether current from a generalized duality symmetry.

The formulation includes helicity, spin, and infra-zilch conservation laws.

Abstract

In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al., including helicity, spin, and the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.