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Title: A five-dimensional perspective on the Klein–Gordon equation

Abstract

We discuss the Klein–Gordon (KG) equation using a path-integral approach in 5D space–time. We explicitly show that the KG equation in flat space–time admits a consistent probabilistic interpretation with positively defined probability density. However, the probabilistic interpretation is not covariant. In the non-relativistic limit, the formalism reduces naturally to that of the Schrödinger equation. We further discuss other interpretations of the KG equation (and their non-relativistic limits) resulting from the 5D space–time picture. Finally, we apply our results to the problem of hydrogenic spectra and calculate the canonical sum of the hydrogenic atom.

Authors:
Publication Date:
OSTI Identifier:
22451165
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 356; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; KLEIN-GORDON EQUATION; MANY-DIMENSIONAL CALCULATIONS; PATH INTEGRALS; PROBABILISTIC ESTIMATION; SCHROEDINGER EQUATION; SPACE-TIME

Citation Formats

Breban, Romulus, E-mail: breban@gmail.com. A five-dimensional perspective on the Klein–Gordon equation. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.02.028.
Breban, Romulus, E-mail: breban@gmail.com. A five-dimensional perspective on the Klein–Gordon equation. United States. doi:10.1016/J.AOP.2015.02.028.
Breban, Romulus, E-mail: breban@gmail.com. Fri . "A five-dimensional perspective on the Klein–Gordon equation". United States. doi:10.1016/J.AOP.2015.02.028.
@article{osti_22451165,
title = {A five-dimensional perspective on the Klein–Gordon equation},
author = {Breban, Romulus, E-mail: breban@gmail.com},
abstractNote = {We discuss the Klein–Gordon (KG) equation using a path-integral approach in 5D space–time. We explicitly show that the KG equation in flat space–time admits a consistent probabilistic interpretation with positively defined probability density. However, the probabilistic interpretation is not covariant. In the non-relativistic limit, the formalism reduces naturally to that of the Schrödinger equation. We further discuss other interpretations of the KG equation (and their non-relativistic limits) resulting from the 5D space–time picture. Finally, we apply our results to the problem of hydrogenic spectra and calculate the canonical sum of the hydrogenic atom.},
doi = {10.1016/J.AOP.2015.02.028},
journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 356,
place = {United States},
year = {2015},
month = {5}
}