2005/10/19 by José B. Almeida, Jose B. Almeida, Almeida, Jose B. · 2 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0510179
4 pages
arxiv created 2005/10/19 · openalex publication_date 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the geometry of 5-dimensional spacetime, where monogenic functions are studied. Monogenic functions verify a very simple first order differential equation and the paper demonstrates how they generate the line interval of special relativity, as well as the Dirac equation of quantum mechanics. Monogenic functions act as a unifying principle between those two areas of physics, which is in itself very significant for the perception one has of them. Another consequence is the possibility of studying the same phenomena in Euclidean 4-dimensional space, providing a different point of view to physics, from which one has an unusual and enriching perspective.