It is one of the most surprising result appearing along that quest. The coherence of an investigation incorporating the second order variations of the basis vectors give rise to spinors (*extern link Wikipedia-GB). That means that one must manage a Clifford’s algebra* and that the theory introduces EM-like fields that obviously have a geometrical origin.

 

If they are not a kind of ghost (example: Faddeev-Popov ghosts*), they are of the greatest importance for the modern researches because they offer a natural link between the Maxwell’s theory for electromagnetism* and topological considerations.

 

A deeper analysis of the calculations exhibits the fact that these EM-like fields are deeply related to the Riemann’s-like tensor of that GTR2 approach (see my document below).

 

Noon, as explained in the foundations, each cube involved in that toy-theory is a set of projectors and it is not certain that it coincides with a Christoffel’s cube. I prefer to think about each of them as a generic T-cube. A pertinent interpretation can then be obtained within E. Cartan’s work (1933) on evolutive surfaces (these surfaces generate metrics). Thus, the Riemann’s-like tensor of the GTR2 approach is built with a generic T-cube; exceptionally, it may perhaps coincide with the Christoffel’s cube (this point has been clarified in the French version of the analysis – see the introductory remarks). Please discover and check.

 

© Thierry PERIAT, 09 January 2019.   

 

 

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