On the geometrical aspects of electromagnetism,I |
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Authors: | Marie Fontaine Pierre Amiot |
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Affiliation: | Laboratoire de Physique Nucléaire, Département de Physique, Université Laval, Québec G1K 7P4, Canada |
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Abstract: | The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′μ. The nonlinearity is traded in for the correct characteristic of the test particle through a gauge condition, imposed upon A′μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the ratio inside the gauge leaves F′μν independent of and allows its identification with the E.-M. tensor Fμν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the ratio. |
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