Geometry

   

Non-Euclidean Metric Using Geometric Algebra

Authors: Jesus Sanchez

The Geometric Algebra is a tool that can be used in different disciplines in Mathematics and Physics. In this paper, it will be used to show how the information of the Non-Euclidean metric in a curved space, can be included in the basis vectors of that space. Not needing any external (out of the metric) coordinate system and not needing to normalize or to make orthogonal the basis, to be able to operate in a simple manner. The different types of derivatives of these basis vectors will be shown. In a future revision, the Schwarzschild metric will be calculated just taking the derivatives of the basis vectors to obtain the geodesics in that space. As Annex, future developments regarding GA are commented: rigid body dynamics, Electromagnetic field, hidden variables in quantum mechanics, specificities of time basis vector, 4π geometry (spin 1/2) and generalization of the Fourier Transform.

Comments: 32 Pages.

Download: PDF

Submission history

[v1] 2019-09-20 13:18:03
[v2] 2019-09-22 10:12:59

Unique-IP document downloads: 22 times

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