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Ciência e Natura

A note on Riemannian geometry and the relativistic quantum mechanics context

Fabio Botelho

Published Dec 7, 2018• 0 citations
Publisher

Abstract

This article develops a variational formulation for relativistic quantum mechanics. The main results are obtained through a connection between relativistic and quantum mechanics. Such a connection is established through basic concepts on Riemannian geometry and related extensions for the relativistic context.
DOI
10.5902/2179460x34165

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This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the quantum mechanics one. For the second part of the text, the definition of normal field and its relation with the wave function concept play a fundamental role in the main results establishment. Among the applications, we include a model with the presence of electromagnetic fields and also the modeling of a chemical reaction. Finally, in the last section, we present some results about the Spin operator in a relativistic context.
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