Abstract
Clifford algebra as an approach of geometrization of physics plays a vital role in unification of micro-physics and macro-physics, which leads to examine the problem of motion for different objects. Equations of charged and spinning of extended objects are derived. Their corresponding deviation equations as an extension of geodesics and geodesic deviation of vectors in Riemannian geometry have been developed in case of Clifford space.
Highlights
Clifford algebra as an approach of geometrization of physics plays a vital role in unification of micro-physics and macro-physics, which leads to examine the problem of motion for different objects
Due to richness of these quantities this type work will be going to examine the behavior of extended objects subjects having sensitivity to these quantities in our future work ; while in our present work we focus on deriving the equations of motion and their deviation paths for different extended objects spinning and charged for poly-vectors defined within the context of Riemannian-like C-Space as explained
As an introductory step to the C-space formalism obtained by CastroPavsic [18], it is worth to mention that Pezzaglia had presented a speculative vision about the need to utilize Clifford space, the problem of unification can be passed by stages of composing scalar, vectors and bi-vectors in one form with taking into consideration that the corresponding bases vectors are described in non-orthonormal curved space in the following way [11]
Summary
Following the geometrization scheme of physics, a new elegant formalism has been performed, which may explore new hidden physics to show an insightful vision for revisiting the old notations of physics. Such a trend is a crystal clear using Clifford Algebra which leads to express many physical quantities in a compact form [22]. Due to the richness of Clifford algebra, scalars, vectors, bi-vectors and r-vectors are expressed in one form called Clifford aggregate or poly-vector. Where the component s is the Clifford scalar components of a polyvector valued coordinates. In C-space proper time interval may be described as in Minkowski space [18]
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