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**US-GB-version**
Because the mathematical language is international

**US-GB-version**

*© 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.