A five-dimensional perspective on the Klein–Gordon equation

Journal Article · Fri May 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.02.028· OSTI ID:22451165

Breban, Romulus

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.

• OSTI ID: 22451165
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 356; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
KLEIN-GORDON EQUATION
MANY-DIMENSIONAL CALCULATIONS
PATH INTEGRALS
PROBABILISTIC ESTIMATION
SCHROEDINGER EQUATION
SPACE-TIME