The extrinsic method
is a mathematical method; see the document below. It is a very helpful tool to get answers to the so-called (E) question. The (E) question is: “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)
In physics, I have applied this method in two domains:
– The geodesic deviation equation for weak gravitational fields; see the page: “Motivations for a thesis”.
– The Heisenberg’s uncertainty principle; discover the document: “A. Einstein versus W. Heisenberg”.
Applications (in the literature)
In the community, I newly 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 Lorentz force density (alias Lorentz-Einstein force in my semantic) with the extrinsic method when the geometry is invariant (see more details in my document ISBN… 031-1).
F = – G-1. H
Where G represents the local non-degenerated four-dimensional metric and H a quasi-classical Hessian of which the interpretation is related to an EM potential.
My hope is to have been able to convince the readers that that method can have some advantages in physics.
© Thierry PERIAT, 07 January 2019.