EM fields and geometry

Electromagnetic fields mimicking infinitesimal variations of the geometry.

The theory of deformed tensor products brings a new generic formulation for any electromagnetic (EM) fields in a context where particles are moving in respecting the Lorentz-Einstein law of motion “at the quantum limit”. These fields have remarkably interesting properties as it has already been suggested in the document ISBN 978-2-36923-085-4 below (2016): there are EM fields resembling infinitesimal anti-symmetric variations of the geometry.

[F] = δ[G]

That document was until now a stand-alone piece in the puzzle of my investigations. The recent lecture of [01] gives me 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 “When Christoffel meets Heisenberg” within that Cauchy’ problem.

E. Cartan’ work on spinors [02] 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 γ2 or the γ5 Dirac’ matrix (Freeman Dyson convention).

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.

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event Date de dernière mise à jour : 25/10/2020

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