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

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

18 pages, 2 figures. Partly reproduces the old (unpublished) preprint arXiv:gr-qc/0012109

References in corpus (2)

• Algbrodynamics over complex space and phase extension of the Minkowski geometry
• Three kinds of particles on a single rationally parameterized worldline

Cited by in corpus (1)

• Gauge origin of the Dirac field and singular solutions to the Dirac equation