Path and Path Deviation equations of Fractal Space-Times: A Brief Introduction

TL;DR

This paper derives geodesic and deviation equations in fractal space-times using the Bazanski method, extending to spinning particles, thus advancing the understanding of motion in fractal geometries.

Contribution

It introduces a method to derive geodesic and deviation equations in fractal space-times and extends this to spinning particles, a novel approach in this field.

Findings

Derived geodesic equations in fractal space-times

Extended equations to spinning and charged particles

Provided a framework for motion analysis in fractal geometries

Abstract

The idea that the quantum space-time of microphysics may be fractal everywhere was intensively investigated recently, and several authors have presented the geodesic equations of different fractal space - times. In the present work we obtain the geodesic and the geodesic deviation equations in fractal space-times by using the Bazanski method. We also extend this approach to obtain the equations of motion for spinning and spinning charged particles in the above-mentioned spaces, in a similar way to their counterparts in Riemannian geometry.