Abstract:
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.