On the helicity of radiative electromagnetic fields

TL;DR

This paper derives a relativistically invariant expression for electromagnetic helicities, demonstrates their conservation in radiative fields, and links quantum helicity to photon spin projections, with applications to dipole pulses.

Contribution

It introduces a new invariant expression for electromagnetic helicities and explores their conservation and quantum interpretation in radiative fields.

Findings

Helicities are conserved and equal in radiative electromagnetic fields.

Electric and magnetic vectors are orthogonal in such fields.

Quantum helicity corresponds to photon spin projections.

Abstract

A relativistically invariant expression for the magnetic and electric helicities of free electromagnetic field through the currents, which created those field, are derived. It is demonstrated that for radiative fields (e.g. laser pulses) the both helicities are conserved and equal to each other. Moreover the conservation of the helicity means that in radiative electromagnetic fields the electric and magnetic vectors are always orthogonal to each other. Proceeding to the quantum theory, it is shown that the corresponding quantum helicity field operator is equal to the sum of projections of spins of all photons onto their momentums. Finally, as an example, the expressions for the total helicity, number of photons and the total spin momentum of the field of a dipole electromagnetic pulse are obtained and discussed.