I finished the basic calculations of paper 439. When putting all parts of Cartan geometry together, we obtain a calculation scheme starting from a potential and ending in electric and magnetic fields of a given physical problem. That is within a framework of general relativity, therefore a novel approach. This is a great progress in ECE theory. Such a complete path had not been carried out before. One reason was that we had not compiled the Cartan formulas in this way so that (at least I myself) did not see that it is possible so straightforwardly. I had looked for this method for years
Another reason is that the Gamma connections can only be computed by computer algebra, and there is the ambiguity of how to choose the appearing constants. Setting them to zero gave an astonishing success in most cases I investigated.
(There remain some problems for complicated potentials. This has to be investigated further and is not addressed in the paper).
One result of the paper is that the B(3) field comes out for e-m waves in a quite natural way. It is lastly a consequence of the fact that the tetrad has to be a non-singular matrix in 4 dimensions. Myron would be delighted
There remains the problem that the Lambda spin connection is not antisymmetric. Either there is still an error in the calculations, or it has to do with the charge density. For e-m waves, which correspond to the e-m free field, all connections are antisymmetric.
I separated the Maxima code in a way that a library for all operations of Cartan geometry needed has been built. This should also be usable for the text book. In addition, this seems to be the begin of a generally usable code which Sean MacLachlan requested a long time ago.
I think we make progress in theory now. I appended the draft version of paper 439. The conclusion is still missing. I will give a perspective for the next papers where the new code path through Cartan geometry could be modified for solving new questions. For example,
1) when the e-m fields are given, what are the connections, and what is the potential (or tetrad)?
2) how can a resonant spin connection be obtained from a given e-m field?