Motion of Poly-vectors in Fractal Clifford Spaces

TL;DR

This paper explores the motion of poly-vectors in fractal Clifford spaces, proposing a new approach to unify micro- and macro-physics through fractal space-time and specialized Lagrangians.

Contribution

It introduces a novel framework using fractal Clifford spaces and poly-vectors to describe trajectories and deviations of extended objects, relaxing differentiability conditions.

Findings

Poly-vector trajectories in FCS are formulated.

Deviation equations for various objects are derived.

A specialized Bazanski Lagrangian for fractal space-time is proposed.

Abstract

Fractal Clifford Spaces (FCS) may be considered as a challenging approach to the unification of micro-physics and macro-physics. Trajectories of these manifolds are described by different poly-vectors describing paths and their deviation equations for not only to test particles but also for charged, rotating and rotating charged objects. Due to relaxing the condition of differentiability for all extended objects in the manifold. In this approach, a specialized Bazanski Lagrangian will be discussed to describe the fractal version of extended objects in a fractal space-time.