2019/10/31 by Ivan Fernandez-Corbaton
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #Electromagnetic field #Electromagnetic tensor #Helicity #Invariant (physics) #Magnetic helicity #Maxwell's equations #Photon #Quantum and Classical Electrodynamics #math-ph #math.MP #physics.optics
paper · pdf · doi:10.3390/sym11111427
published as Symmetry 2019, 11(11), 1427; https://doi.org/10.3390/sym11111427
openalex publication_date 2019/11/19 · arxiv created 2019/11/20 · arxiv updated 2019/11/21 · openalex created_date 2019/12/05 · openalex updated_date 2026/08/06
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in ( r , t ) space, and in the time-harmonic ( r , ω ) space are obtained, featuring Riemann–Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials.