OK, he responds:
“I think not.
As I remember from my paper Microgeon 1974 ,
the complex scalar field \phi = 1/(tilde r)   generates complex 3-vector of em strength  E+iH = grad \phi.
The 4-vector cannot be represented as gradient of scalar.
A^\mu = (1/\tilde r) k^\mu, where k^\mu is a bilinear form proportional to tetrad direction e^3 .”
k^\mu \sim  e^3 = du +Y d ksi* +Y* d ksi + YY* dv
I answer, ‘I will see today.’ Slowly I turn the crank on this great, beautiful machine. . ‘OK, I think not also. The RULES being what they are, we take
gradients, of REAL and IMAGINARY… I stay with my thesis, that
POTENTIAL FORMS in such a non-integrable space, are not usable. I am
curious, with Appel’s identification of  E + iH, what happens with the
rest of the 4-vector potential form…’


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