The implications of introducing Proca equations include an alternative description of superconductivity, via extending London equations.
The implications of introducing Proca equations include description of superconductivity, by extending London equations .
The background argument of Proca equations can be summarized as follows .
Therefore, it seems plausible to extend further the Maxwell-Proca equations to biquaternion form too; see also [9, 10] for links between Proca equation and Klein-Gordon equation.
In this regards, it has been shown by Sternberg , that the classical London equations for superconductors can be written in differential form notation and in relativistic form, where they yield the Proca equations.
Similarly in this regards, in a recent paper Tajmar has shown that superconductor equations can be rewritten in terms of Proca equations .
With a nonzero photon mass, the usual Maxwell equations transform into the so-called Proca equations which will form the basis for our assessment in superconductors and are only valid for the superconducting electrons.
Therefore the basic Proca equations for superconductor will be [19, p.
Nonetheless, the use of Proca equations have some known problems, i.
Using the method we introduced for Klein-Gordon equation , then it is possible to generalize further Proca equations (1) using biquaternion differential operator, as follows: