Summary
The notion of helicity for the free electromagnetic field is analysed. The generalized helicity is introduced which is a conserved quantity coinciding with the difference of the right and left circularly polarized photons composing the electromagnetic field. It seems that it completes the list of the zilch-type invariants found by Lipkin and Ragusa. The gauge-invariant expression for the energy of the free gravitational field is obtained which strongly resembles the well-known bilinear expression for the total number of photons composing the electromagnetic field.
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Afanasiev, G.N., Stepanovsky, Y.P. The helicity of the free electromagnetic field and its physical meaning. Nuov Cim A 109, 271–279 (1996). https://doi.org/10.1007/BF02731014
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DOI: https://doi.org/10.1007/BF02731014