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arXiv · 1910.13927

A conformally invariant derivation of average electromagnetic helicity

Ivan Fernandez-Corbaton
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Abstract

The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. In here, the average helicity is derived using the conformally-invariant inner-product for Maxwell fields. Several equivalent integral expressions in momentum space, in $(\mathbf{r},t)$ space, and in the time-harmonic $(\mathbf{r},\omega)$ 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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Ivan Fernandez-Corbaton. 2019-10-30. A conformally invariant derivation of average electromagnetic helicity. https://doi.org/10.3390/sym11111427

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