The extrinsic method


See the document below: (247.41 Ko)



is another mathematical method to get answers to the so-called (E) question: “Consider a deformed tensor product (DTP) in E(D, K) where usually K represents either R or C. Consider the image of that DTP in the dual space E*(D, K) of E(D, K). How can I divide it and get a pair ([P], z) in M(D, K) x E(D, K)?”

Applications (personal propositions and contributions)

In physics, I have applied this method in a four-dimensional context, in two domains:

  • The geodesic deviation equation for weak gravitational fields.
  • The Heisenberg’s uncertainty principle. This application simultaneously concerns E. B. Christoffel’s work and the covariant version of the Lorentz law. It can be discovered on the page: “A. Einstein versus W. Heisenberg”.

Applications (in the literature)

In the community, I discovered an article (under the Common Creative licence) titled:

  • “Quantum effective action for degenerate vector field theory“ published on the 17th October 2018 by the American Physical Society in Phys. Rev. D 98, 085014 (2018)” in which the formula (5) has exactly the formalism induced by the analysis of the covariant Lorentz law (giving the force density for electrical particles moving in a gravitational field) with the extrinsic method when the geometry is invariant; see more details in my document ISBN… 031-1 on the page EM fields after A. Einstein versus W. Heisenberg or in the document ISBN… 035-9 on the French part of this website.

F = - G-1. H

Where G represents the local non-degenerated four-dimensional metric and H a quasi-classical Hessian.

© Thierry PERIAT

Go back to the page: “English presentation”.

event Date de dernière mise à jour : 09/09/2020