# The chameleons fields

**The document: **The chameleons fields (623.7 Ko).

The previous exploration has proposed a totally new logical path between the theory of relativity (A. Einstein’s work; alias: GTR) and W. Heisenberg’s uncertainty principle (extern link Wikipedia – GB) in a full four-dimensional context.

The link is obtained with a specific treatment of the Lorentz-Einstein Law of motion involving a procedure allowing the decomposition of deformed tensor (resp. Lie) products. It yields a specific and new expression for the (2, 0) representation of the EM fields.

This expression is important because it contains terms depending on the local four-dimensional metric and on its variations. Just because of that fact, it can be suspected that EM fields have permanent interaction with the geometry. Hence, the new formulation should be able to give indications on the intensity of the interactions between both types of fields.

In this document, I prove that, when the EM fields can be written as explained in “A. Einstein versus W. Heisenberg”, then they may sometimes be equivalent to small variations of the geometry. This is the reason why I have called that part of my explorations: “The subtle interplay between the EM fields and the geometry”. This is not a new document (2016), but it contains interesting and pedagogical information about the links between EM fields, spinors (see extern link Wikipedia – GB) and gravitation.

**Consequences**

That document was until now a stand-alone piece in the puzzle of my investigations. The lecture of [01] gives the opportunity to resituate this work in a better-founded mathematical and physical context; precisely inside a specific Cauchy’ problem.

The document reveals the conditions allowing to interpret the generic formalism of the EM fields which are predicted by the approach “Einstein versus Heisenberg” within that Cauchy’ problem.

E. Cartan’ work on spinors [02] also plays a crucial role in the demonstration. The initial metric must be symmetric, and the trivial dilatation of the four-speed must be proportional to either the gamma2 or the gamma5 Dirac’ matrix (Freeman Dyson convention [03]).

Although the strange formula is seemingly acceptable, the evolutions of these metrics and of the corresponding pseudo-EM fields must yet be investigated.

© Thierry PERIAT

**Bibliography**:

[01] On isometric immersions of a Riemannian space under weak regularity assumptions, C. R. Acad. Sci. Paris, Ser. I 337, 2003, 785-790.

[02] Cartan, E. The theory of spinors. First published by Hermann of Paris in 1966; translation of the ``Leçons sur la théorie des spineurs (2 volumes)''; Hermann, 1937; Dover Publications, Inc. New York. © 1966 by Hermann, Paris, ISBN 0-486-64070-1; 151 pages.

[03] D. Freeman: Quantenfeld-theorie (Die Weltbekannte Einführung von einem der Väter der QED); Springer Spektrum, ISBN 978-3-642-37677-1, © Springer Verlag Berlin Heidelberg 2014..

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*event* Last edited: 20/11/2020