Helmholtz' decomposition and neutrinos


Abstract of the French version (ISBN 978-2-36923-098-4 in preparation)

In prior documents I started to explore the concept of derivation (see on the French part). In that document I ask a seemingly simple question: ``Can the variations of a vectorial function f be equivalent to a classical cross product q x dx in E(3, K = R or C)? If yes: when?''

An harmonious mixture between the intrinsic and the extrinsic methods brings the answer to that question. In peculiar, when the two polynomials (one for each method: the intrinsic Lambda and the extrinsic P1) depending on the components of the projectile (see my semantic) are not proportional.

These basic results are analyzed with the help of Helmholtz' theorem (extern link Wikipedia-GB). That analysis exhibits two promising links: one between the gradient of some scalar function and the rotational vector of the function f; another one with what the literature calls the democratic matrices.

These matrices are wellknown in the branch of physics studying the masses of neutrinos (seesaw mechanism; extern link Wikipedia-GB). This fact encourages me to look for generic representations of polynomials in M(4, K) and is a strong motivation to generalize the links between both types of polynomials (i.e.: when the intrinsic and the extrinsic one are no more proportional to each other).

The work is going on. That analysis is suggesting a rationalistic mathematical path explaining the origin of neutrinos masses in a context where these particles are understood as part of some energetic flow.

Copyright by Thierry PERIAT, first published 18 October 2020.

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event Date de dernière mise à jour : 20/10/2020