A New Class of Path Equations in AP-Geometry

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.Comment: 11 pages, LaTeX fil

Space-Time Structure and Electromagnetism

Two Lagrangian functions are used to construct geometric field theories. One of these Lagrangians depends on the curvature of space, while the other depends on curvature and torsion. It is shown that the theory constructed from the first Lagrangian gives rise to pure gravity, while the theory constructed using the second Lagrangian gives rise to both gravity and electromagnetism. The two theories are constructed in a version of absolute parallelism geometry in which both curvature and torsion are, simultaneously, non-vanishing. One single geometric object, {\it W-tensor}, reflecting the properties of curvature and torsion, is defined in this version and is used to construct the second theory. The main conclusion is that a necessary condition for geometric representation of electromagnetism is the presence of a non-vanishing torsion in the geometry used.Comment: 17 pages, LaTeX file, revised versio

An Alternative Source for Dark Energy

In the present work, an alternative interpretation of the source of accelerated expansion of the Universe is suggested. A probable candidate is the interaction between the quantum spin of a moving particle and the torsion of space-time, produced by the background gravitational field of the Universe. This interaction has been suggested by the author in a previous work, with some experimental and observational evidences for its existence. It has been shown that this interaction gives rise to a repulsive force. The accelerated expansion of the Universe may give a further evidence on the existence of this interaction on the cosmological scale.Comment: 3 pages, LaTeX file, summary of a talk delivered at MG XI, held in Berlin, July 200