A note on Riemannian geometry and the relativistic quantum mechanics context

Fabio Silva Botelho

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.

Keywords


Quantum mechanics; Riemannian geometry; Klein-Gordon equation

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References


R.A. Adams and J.F. Fournier, Sobolev Spaces, 2nd edn. (Elsevier, New York, 2003).

D. Bohm, A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables I, Phys.Rev. 85, Iss. 2, (1952).

D. Bohm, Quantum Theory (Dover Publications INC., New York, 1989).

F. Botelho, Functional Analysis and Applied Optimization in Banach Spaces, (Springer Switzerland, 2014).

F. Botelho, Real Analysis and Applications, (Springer Switzerland, 2018).

B. Hall, Quantum Theory for Mathematicians (Springer, New York 2013).

L.D. Landau and E.M. Lifschits, Course of Theoretical Physics, Vol. 5- Statistical Physics, part 1. (Butterworth-Heinemann, Elsevier, reprint 2008).

S.Weinberg, Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity, Wiley and Sons, (Cambridge, Massachusetts, 1972).




DOI: http://dx.doi.org/10.5902/2179460X34165

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