{"title":"A General Variational Formulation for Relativistic Mechanics Based on Fundamentals of Differential Geometry","authors":"F. Botelho","doi":"10.1201/9781003158912-8","DOIUrl":"https://doi.org/10.1201/9781003158912-8","url":null,"abstract":"The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion manifold has a $n+1$ dimensional range. It is worth emphasizing in a first approximation we have neglected the self-interaction energy part. In its second part, this article develops some formalism concerning the causal structure in a general space-time manifold. Finally, the last article section presents a result concerning the existence of a generalized solution for the world sheet manifold variational formulation.","PeriodicalId":347698,"journal":{"name":"Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122269764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Variational Formulation for the Relativistic Klein-Gordon Equation","authors":"F. Botelho","doi":"10.5902/2179460X33536","DOIUrl":"https://doi.org/10.5902/2179460X33536","url":null,"abstract":"This article develops a variational formulation for the relativistic Klein-Gordon equation.The main results are obtained through a connection between classical and quantum mechanics. Such a connection is established through the definition of normal field and its relation with the wave function concept.","PeriodicalId":347698,"journal":{"name":"Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125518273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}