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Open AccessArticle

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 ( 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. View Full-Text
Keywords: electromagnetic helicity; conformal symmetry electromagnetic helicity; conformal symmetry
MDPI and ACS Style

Fernandez-Corbaton, I. A Conformally Invariant Derivation of Average Electromagnetic Helicity. Symmetry 2019, 11, 1427.

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