Abstract
Using a geometry wider than Riemannian one, the parameterized absolute parallelism (PAP) geometry, we derived a new curve containing two parameters. In the context of the geometrization philosophy, this new curve can be used as a trajectory of charged spinning test particle in any unified field theory constructed in the PAP space. We show that imposing certain conditions on the two parameters, the new curve can be reduced to a geodesic curve giving the motion of a scalar test particle or/and a modified geodesic giving the motion of neutral spinning test particle in a gravitational field. The new method used for derivation, the Bazanski method, shows a new feature in the new curve equation. This feature is that the equation contains the electromagnetic potential term together with the Lorentz term. We show the importance of this feature in physical applications.
Highlights
According to the geometrization philosophy, the curve in a certain geometry represents the equation of motion of a theory which constructed in this geometry
Geodesic curve is considered as an equation of motion of a scalar test particle moving in a gravitational field
This work is carried out in the context of the “parameterized absolute parallelism” (PAP) geometry abbreviated as ðM, λÞ
Summary
According to the geometrization philosophy, the curve in a certain geometry represents the equation of motion of a theory which constructed in this geometry. This property motivates Wanas [7] to consider the right hand side of the above set of equations as representing a geometric interaction between the quantum spin of the moving particle and the torsion of the background geometry For this property, Wanas generalized the AP space by constructing a new version called the parameterized absolute parallelism (PAP). Applying the modified Bazanski approach in the context of PAP geometry, Wanas [7] obtained a modified geodesic equation This equation describes the motion of a spinning particle moving in a gravitational field. In the framework of PAP geometry, we are going to derive the equation of motion of a spinning and charged particle moving in a combined gravitational and electromagnetic field (a unified field), using the modified Bazanski approach
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