Applications for the extrinsic method

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

• A confrontation between E. B. Christoffel’s, Einstein’s and Heisenberg’s 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”.
• An analysis linking the Klein-Gordon equation with the covariant version of the Lorentz law.

Presence of similar results 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 of 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

G represents the local non-degenerated four-dimensional metric and H is a quasi-classical Hessian. That equation exhibits the same formalism than some generic decomposition of the gravitational term appearing in the covariant version of the Lorentz law when its trivial part vanishes.