A Conformally Invariant Derivation of Average Electromagnetic Helicity
Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
Symmetry 2019, 11(11), 1427; https://doi.org/10.3390/sym11111427
Received: 14 October 2019 / Revised: 5 November 2019 / Accepted: 8 November 2019 / Published: 19 November 2019
(This article belongs to the Special Issue Duality Symmetry)
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 space, and in the time-harmonic 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.
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Keywords:
electromagnetic helicity; conformal symmetry
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MDPI and ACS Style
Fernandez-Corbaton, I. A Conformally Invariant Derivation of Average Electromagnetic Helicity. Symmetry 2019, 11, 1427.
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