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General Solution of the Complex 4-Eikonal Equation and the "Algebrodynamical" Field Theory

Vladimir V. Kassandrov
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Abstract

We explicitly demonstrate the existence of twistor and ambitwistor structure for the 4-dimensional complexified eikonal equation (CEE) and present its general solution consisting of two different classes. For both, every solution can be obtained from a generating twistor function in a purely algebraic way, via the procedure similar to that used in the Kerr theorem for shear-free null congruences. Bounded singularities of eikonal or of its gradient define some particle-like objects with nontrivial characteristics and dynamics. Example of a new static solution to CEE with a ring-like singularity is presented, and general principles of algebraic field theory - algebrodynamics - closely related to CEE are briefly discussed.

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Vladimir V. Kassandrov. 2003-11-05. General Solution of the Complex 4-Eikonal Equation and the "Algebrodynamical" Field Theory. https://arxiv.org/abs/math-ph/0311006

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