A New Class of Path Equations in AP-Geometry

Details A New Class of Path Equations in AP-Geometry A New Class of Path Equations in AP-Geometry

2004-08-11

arxiv.org/abs/gr-qc/0408029v3

Int.J.Geom.Meth.Mod.Phys.2:1017-1027,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, LaTeX file

Scientific paper

10.1142/S021988780500096X

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov-Bohm effect. It is to be considered that all extra terms will vanish if the space-time used is torsion-less.

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