Quelques rêveries cosmiques cosmoquant-fr

Geometry-and-bivectors

Title: Does the new formalism of the EM field tensor contain a bivector à la E. Cartan?

Author: © Thierry PERIAT.

French matriculation: ISBN 978-2-36923-085-4, EAN 9782369230854.

Language: GB/USA.

Version: 1-3.

Publication: 17 November 2022.

Number of pages: 19.

Nom du fichier : Isbn 978 2 36923 085 4 periat

Taille : 629.13 Ko

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Comments.

Another exploration [ISBN 978-2-36923-026-7; French language] has proposed a totally new logical path between the theory of relativity (A. Einstein’s work; alias: GTR) and W. Heisenberg’s uncertainty principle in a full four-dimensional context.

The link is obtained with a specific treatment of the Lorentz-Einstein Law (synonym: covariant version of the Lorentz law). The procedure lies on a mathematical method (the so-called extrinsic one) working by approximation. It can propose a generic formalism for the decomposition of deformed tensor (resp. Lie) products. In peculiar, it yields a specific and new expression for the (2, 0) representation of the electromagnetic (EM) fields: see inside the document.

This expression is important because it is formally suggesting that EM fields have permanent interactions with the geometry or, also quite interesting, that EM field can emerge due to variations of the geometry.

Hence, the question is: "Does the EM field tensor which has been obtained in analyzing the Lorentz-Einstein law with the extrinsic method represent a variation of the geometry?"

The aim of this document is to discover some consequences of that formalism.

The exploration will reveal an unexpected direct link between the skew symmetric variations of the geometry and a specific family of EM-fields. E. Cartan’s work on spinors plays a crucial role in this demonstration.

This is the second time within the theory exploring diverse faces of deformed products where the geometry and its variations are directly related to the existence of electromagnetic fields; see the page: “Unifying gravitation and electromagnetism”.

© Thierry PERIAT.

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Date de dernière mise à jour : 17/11/2022