Helicity, spin, and infra-zilch of light: A Lorentz covariant formulation

Sajad Aghapour,Lars Andersson,Kjell Rosquist

doi:10.1016/j.aop.2021.168535

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. (2012), including helicity, spin, as well as 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.

Highlights

The physical relevance of the spin and orbital parts of the angular momentum of the Maxwell field was first demonstrated by Allen et al [2] and van Enk and Nijenhuis [3] in the early 1990’s
We have introduced a new Lorentz covariant tensor, Habc, which we call the helicity tensor, that is conserved in Lorenz gauge, and contains the same information as the helicity array of Cameron et al [1]
The conserved currents expressing helicity, spin, and infra-zilch can be obtained from the helicity tensor by performing a 1 + 3 decomposition and specializing to transverse gauge

Summary

Introduction

The physical relevance of the spin and orbital parts of the angular momentum of the Maxwell field was first demonstrated by Allen et al [2] and van Enk and Nijenhuis [3] in the early 1990’s. The fact that this mapping involves both potentials is an indication that a tensor description of the helicity array is related to a self-dual formulation of Maxwell theory. In particular this is a symmetry of the duality-symmetric Lagrangian with Lorenz gauge fixing terms

The helicity array in Maxwell theory

Helicity tensor in complex duality-symmetric formulation

Noether analysis

Concluding Remarks