Because the mathematical language is international
© Thierry PERIAT: Texts, photos and ideas.
The document ISBN 978-2-36923-024-3 (annex 02) has been moved on the page "Maxwell's vacuum".
The TEQ has a long history.
Although involving a minimal kit of mathematical tools and developing naive demonstrations, the initial document still introduces the basic elements for a deeper and a more fundamental discussion (the cross products: as a trivial illustration for the exterior products and for the Lie products; the matrix representations of rotations: as prehistoric illustration for the future trivial decompositions of the TEQ). Its most impressive achievement lies in a demonstration proving the existence of neutral energetic flows in a very classical Maxwell's vacuum, exactly where nothing should have happened. It also softly introduces what will become the most important idea of my theory: for some unclear reasons, Lie products may eventually be deformed and that idea has immediate consequence in physics; e.g.: in cosmology with the Friedman-Robertson-Walker (FRW) metric and in the conform quantum field theory (CFT) with the concept of flavour exchange as well (see some equations in the document below).
The original version of has been written in the middle of the seventies (physics was already my hobby), after a controversial meeting with the unfortunate advocate of the so-called synergistic theory, just before I decided to start my studies in dentistry (1976-1982). More precisely: at a time where neutral flows (the Zs) had just been predicted by Abdus Salam, Sheldon Glashow and Steven Weinberg (1973) and the masses were not yet known (They only have been available in 1983). Motivated by the positive reactions of some professional working in physics and, in some, way forced by a brain stroke which broke my dentist career, I restarted my research in physics in 2004, scrutinizing the mathematics deeper.
The first step in that way has been guided by two obsessions: (a) the rigorous definition for a generalized (deformed) Lie product (not for the exterior product); (b) the writing of a theory explaining how and why deformed Lie products should be non-trivially decomposed accordingly to local circumstances.
The first English version of that quest concerns only three-dimensional spaces is based on a so-called intrinsic method and can be read on www.researchgate.net. After that, my progression has been stopped during a long time because that method appeared to be a kind of accident, was based on a long demonstration (the initial theorem) which was difficult to check (and nobody was really interested by my crazy work), could not yield the residual part of a decomposition and was only working in a three-dimensional environment!
The situation could slowly change and positively evolve after the discovery of the extrinsic method (working in any dimension) and its confrontation, in a three-dimensional space. The initial goal has only been reached recently (2018) with the strategy explained in a two-dimensional space but working fine in any dimension.
The long progression between 2004 and 2018 is now ending with the GTR2 proposal which is slowly but certainly driving us into the direction of a new concept of Kummer density tensor.
This tool allows reasonable considerations about a possible harmonization between electrodynamics and gravity in a four-dimensional context (which is the environment in which we believe to live in).
The quest of a plausible quantum gravity theory is far to be achieved but it seems to me that the discovery of a convenient four-dimensional space where all known phenomenon can happen was the first necessary step into the whished direction.
A second important information lies in the fact that the GTR2, per essence, is introducing and manipulating angular momentums (via the deformed tensor products the theory is indirectly referring to) which are unavoidable objects in a quantum theory.
The next step in my progression will be an exposé introducing the curvature tensor in an original way via the variations of the deformed tensor products. This will be a reworking of an old work of mine (DU.pdf). I could not start something serious with it, until now. But since the GTR2 introduces curvatures irremediably related to discontinuities, it becomes now clear that, within the TEQ-versus GTR2, gravity is the phenomenon reducing these spatial discontinuities in acting a little bit like a flash of lightning in electricity (nota bene: they are reducing the too strong differences of potential) and as a glue as well.