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Институт Физики Вакуума - Теория

Shipov G.I.
Geometrical and phenomenological torsions
in relativistic physics
Oб авторе

The Ricci and Cartan torsions are compared. Their common properties and distinctions are revealed. It is shown that Ricci torsion determines curvature and torsion in Frenet's equations and consequently the very torsion, instead of the Cartan one, can be connected with spin properties of matter. The theorems showing that in flat and curved spaces it is possible to present Frenet's curves as a first kind geodesic lines of space of absolute parallelism are proved . The connection between fields and forces of inertia and torsion of geometry of absolute parallelism (Ricci torsion) is established.
On the basis of Frenet's equations the structure of radiation friction force in equations of charge motion possessing a spin is investigated. It is shown, that there is a radiation force connected with the charge spin, which is responsible for torsion component of electromagnetic field. The theoretical evaluation of this force magnitude is given. It is concluded, that torsion interactions are weaker than electromagnetic ones, but stronger than gravitational ones.

1. Frenet's equations

In the middle of the last century French mathematician F. Frenet has written famous equations, describing motion of orientable point1 along arbitrary curve x = x(s), where s - the length of an arc.
Frenet's equations are written for normalized on unit orthogonal vectors e1, e2 and e3 with the beginning in a point M ( fig.1). They are as follows [1]

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Shipov G.I. Geometrical and phenomenological torsions in relativistic physics // «Академия Тринитаризма», М., Эл № 77-6567, публ.11657, 19.11.2004

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