Proca equations

Proca equations

[′prō·kə i‚kwā·zhənz]
(quantum mechanics)
A set of equations, analogous to Maxwell's equations, relating a four-vector potential and a second-rank tensor field describing a particle of spin 1 and nonzero mass.
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This book outlines higher form Proca equations on Einstein manifolds with boundary data along conformal infinity, solving these Laplace-type boundary problems formally by constructing an operator which projects arbitrary forms to solutions.
Further extension to Proca equations in Quaternion Space seems possible too using the same method [7], but it will not be discussed here.
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 [18].
The background argument of Proca equations can be summarized as follows [6].
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 [18], 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 [19].
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 [2], then it is possible to generalize further Proca equations (1) using biquaternion differential operator, as follows: