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arXiv · 1612.06718

Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence

Vladimir V. Kassandrov·Joseph A. Rizcallah
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Abstract

We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, $SL(2,\mathbb C)$ Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges ("elementary" for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding "particle-like" field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit non-trivial collective dynamics simulating physical interactions

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Vladimir V. Kassandrov, Joseph A. Rizcallah. 2016-12-19. Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence. https://doi.org/10.1142/s0219887817500311

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