# The extrinsic method

**The document: ISBN 978-2-36923-092-2 **The extrinsic method (351.77 Ko)**.**

**The extrinsic method **

The extrinsic method is another mathematical method to get answers to the so-called (E) question (see the intrinsic method). In opposition with the intrinsic one, the procedure brings a complete result; I mean: a main part and a residual part. Its disadvantages: the result is an approximation and the procedure itself must be counterchecked with a logical test. In fact, the (E) question receives reasonable answers when the methods are confronted. The confrontation realizes a calibration (see further developments).

For now, this method is the starting point for two discussions occurring in a four-dimensional context:

- A confrontation between E. B. Christoffel’, Einstein’ and Heisenberg’ works through the covariant version of the Lorentz law: “A. Einstein versus W. Heisenberg”.
- An interpretation of the geodesic deviation equation for “Weak gravitational fields”.

**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 17
^{th}October 2018 by the American Physical Society in Phys. Rev. D 98, 085014 (2018)” in which the formula (5), i.e.:

F = - G^{-1}. H

has exactly the formalism resulting from the analysis of the covariant version of the Lorentz law (where G represents the local non-degenerated four-dimensional metric and H is a quasi-classical Hessian) .

© Thierry PERIAT.

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Last edited: 22/12/2020