160 research outputs found
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
- …