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Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics

Andrew Chubykalo·Augusto Espinoza·Alvarado-Flores·Alejandro Gutierrez Rodriguez
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Abstract

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.

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Andrew Chubykalo, Augusto Espinoza, Alvarado-Flores, Alejandro Gutierrez Rodriguez. 2005-11-12. Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics. https://doi.org/10.1007/s10702-006-1847-y

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