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

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
Resource Relation:
Journal Name: Annals of Physics; 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)
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