Proca field equations gauge invariance

It should finally be mentioned that the basic equations (l)-(8) have been derived from gauge theory in the vacuum, using the concept of covariant derivative and Feynman s universal influence [38]. These equations and the Proca field equations are shown to be interrelated to the well-known de Broglie theorem, in which the photon rest mass m can be interpreted as nonzero and be related to a frequency v = moc2/h. A gauge-invariant Proca equation is suggested by this analysis and relations (l)-(8). It is also consistent with the earlier conclusion that gauge invariance does not require the photon rest mass to be zero [20,38]. 

In order to derive field equations in the vacuum that are self-consistent, cause must precede effect and the classical current of the Proca current must be gauge-invariant. The starting point for the development is the concept of scalar field... 

The locally gauge-invariant Lehnert field equation corresponding to Eq. (374) was derived as Eq. (350). The photon picks up mass from the vacuum itself, and having derived a locally gauge-invariant Proca equation, canonical quantization can be applied to produce a photon with mass with three space dimensions. 

At the Higgs minimum, this field equation reduces to the locally gauge-invariant Proca equation... 

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