Helmholtz decomposition

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Document : visit the French version of this website or my page on vixra.org.


This document (in the French language) is an attempt looking solutions for the seemingly simple question:

Does q  exists in E(3, K) such that: df = (q x dx) + 0(2) ?

The solutions are reached in mixing the intrinsic method and the extrinsic method. The confrontation realizes a kind of calibration insuring the coherence between both methods. There are in fact two plausible calibrations; one of them is introducing the aera metrics, a concept due to E. Cartan (1933).

They are then analysed with Helmholtz’ decomposition theorem (classical vectorial analysis).

I get several indications suggesting a link between that approach and theories proposing explications for the origin of neutrinos masses. This is not really a surprizing result since this old theorem has now an extension, the Helmholtz-Hodge theorem, acting in any three-dimensional Riemannian space.

The conclusion is that the helicity of neutrinos deserves perhaps more attention.

© Thierry PERIAT.

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Last edited: 10/09/2021