Archive for July, 2019

New forms of handling polarization indices in Cartan geometry

Doug Lindstrom is currently developing a paper on totally antisymmetric torsion. It comes out that the torsion tensor then is homomorphic to a 4-vector. This will give new insights, including a new reduction of polarization indices.
I myself tried out tetrad matrix examples which have diagonal form. This means that the coordinate systems of the base manifold and tangent space are collinear. In terms of Cartan geometry, this means that there is a 1-to-1 correspondence between Greek and Latin indices. As a next step, I will develop the e-m field from torsion (which is simply a re-numbering of torsion tensor elements). The tetrad is the e-m potential, and a diagonal tetrad means that there is exactly one scalar potential and one vector potential. We will see if meaningful results will follow from this approach.

New textbook on ECE theory in preparation

As you all know I am working on the ECE text book. I have finished now the first three chapters: introduction, mathematical foundations and geometrical identities of Cartan geometry. I worked out the proofs of the Cartan-Bianchi and Cartan-Evans identity. The latter is the Hodge dual of the Cartan-Bianchi identity which is the usual Bianchi identity including torsion. I have spent some time to work out computational examples. So the validity of both identities is shown by Maxima code examples. The code is usable for any tetrad matrix and fully general. Myron would have been delighted about this. I ask you for some patience, until the proofreading is finished. Then we will have a little mathematical textbook for studying Cartan geometry. Of course this is not yet ECE theory. The axioms of ECE theory, ECE2 and electrodynamics will follow. Then a reader can get a fuller grasp of ECE.

Plans for next papers

Paper 438 will be finished in memoriam of Myron. I have still to do some calculations on the escape velocity from dark stars. For paper 437 section 3 is missing, I will have to alter the quantum chemistry program for atoms to get some results. Concerning new papers, we could think about the time development of the universe, described by m theory. This will require some discussions and notes in advance.

AIAS work goes on

The development of ECE theory will be continued by AIAS. After the sudden death of Myron Evans, progress will be less rapid, but the AIAS members will continue theoretical and practical work on ECE theory.