Electromagnetic theory field divergence

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

The extra degree of freedom introduced into the present theory by the nonzero electric field divergence gives rise to new classes of phenomena such as bound steady electromagnetic equilibria and free dynamic states, including wave phenomena. These possibilities are demonstrated by Fig. 1. 

Figure 2. The three fundamental wave types of an extended electromagnetic theory with nonzero electric field divergence in the vacuum, as demonstrated by the simple case of plane waves.

These four fundamental equations of electromagnetic theory can be very elegantly expressed in terms of the vector operators divergence and curl. The first Maxwell s equation is a generalization of Coulomb s law for the electric field of a point charge ... 

It is not possible for conventional electromagnetic models of the electron to explain the observed property of a point charge with an excessively small radial dimension [20]. Nor does the divergence in self-energy of a point charge vanish in quantum field theory where the process of renormalization has been applied to solve the problem. 

The divergence of the gradient of a scalar field occurs in several fundamental equations of electromagnetism, wave theory, and quantum mechanics. In Cartesian coordinates. 

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