Potential Lienard-Wiechert

The Lienard-Wiechert potentials (12) can also be derived from a rotation-free Lorentz transformation (boost) of the four potential of a static charge (13) to the moving frame at retarded time. For a charge moving at constant velocity the potentials can also be expressed in terms of the current position giving [21]... 

As the only explicit time-dependent solution of Cauchy s problem, the Lienard-Wiechert potentials are claimed be inadequate for describing... 

The approach by Chubykalo and Smirnov-Rueda further includes longitudinal modes and Coulomb long-range electromagnetic fields that cannot be described by the Lienard-Wiechert potentials [2,57]. 

In their considerations on the field generated by a single moving charged particle, Chubykalo and Smimov-Rueda [2,56,57] have claimed the Lienard-Wiechert potentials to be incomplete. These potentials are then not able to describe long-range instantaneous Coulomb interaction. However, in a modified theory by Chubykalo and Smimov-Rueda such interaction is included. The applicability of these potentials is, however, still under discussion [9]. 

In the particular case of a moving charge the retarded potentials are given by the Lienard-Wiechert potentials... 

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