A variational formulation for relativistic mechanics based on Riemannian geometry and its application to the quantum mechanics context

2018/12/07 by Fabio Botelho, Botelho, Fabio
Mathematics · Physics and Astronomy · #49Q99 #49S05 #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AP #msc:49Q99 #msc:49S05

paper · pdf · doi:10.48550/arxiv.1812.04097

16 pages, new results based on the Weinberg approach for relativistic mechanics, one more section added

openalex publication_date 2018/12/07 · arxiv created 2019/06/12 · arxiv updated 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and connection have a fundamental role in the main action establishment. In the last section, as a result of an approximation for the main formulation, we obtain the relativistic Klein-Gordon equation.

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