Stability in the instantaneous BetheSalpeter formalism: Harmonicoscillator reduced Salpeter equation
Abstract
A popular threedimensional reduction of the BetheSalpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all boundstate constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of the problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonicoscillator confining interactions. There we are able to prove rigorously that the boundstate solutions correspond to real discrete spectra bounded from below and are thus free of all instabilities.
 Authors:

 Faculty of Physics, University of Vienna, Boltzmanngasse 5, A1090 Vienna (Austria)
 Publication Date:
 OSTI Identifier:
 21024093
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 76; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.76.125028; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BETHESALPETER EQUATION; BOUND STATE; ENERGY SPECTRA; HARMONIC OSCILLATORS; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; STABILITY; THREEDIMENSIONAL CALCULATIONS; VARIATIONAL METHODS
Citation Formats
Zhifeng, Li, Lucha, Wolfgang, Schoeberl, Franz F, Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A1050 Vienna, and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A1090 Vienna. Stability in the instantaneous BetheSalpeter formalism: Harmonicoscillator reduced Salpeter equation. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.76.125028.
Zhifeng, Li, Lucha, Wolfgang, Schoeberl, Franz F, Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A1050 Vienna, & Faculty of Physics, University of Vienna, Boltzmanngasse 5, A1090 Vienna. Stability in the instantaneous BetheSalpeter formalism: Harmonicoscillator reduced Salpeter equation. United States. https://doi.org/10.1103/PHYSREVD.76.125028
Zhifeng, Li, Lucha, Wolfgang, Schoeberl, Franz F, Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A1050 Vienna, and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A1090 Vienna. Sat .
"Stability in the instantaneous BetheSalpeter formalism: Harmonicoscillator reduced Salpeter equation". United States. https://doi.org/10.1103/PHYSREVD.76.125028.
@article{osti_21024093,
title = {Stability in the instantaneous BetheSalpeter formalism: Harmonicoscillator reduced Salpeter equation},
author = {Zhifeng, Li and Lucha, Wolfgang and Schoeberl, Franz F and Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A1050 Vienna and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A1090 Vienna},
abstractNote = {A popular threedimensional reduction of the BetheSalpeter formalism for the description of bound states in quantum field theory is the Salpeter equation, derived by assuming both instantaneous interactions and free propagation of all boundstate constituents. Numerical (variational) studies of the Salpeter equation with confining interaction, however, observed specific instabilities of the solutions, likely related to the Klein paradox and rendering (part of the) bound states unstable. An analytic investigation of the problem by a comprehensive spectral analysis is feasible for the reduced Salpeter equation with only harmonicoscillator confining interactions. There we are able to prove rigorously that the boundstate solutions correspond to real discrete spectra bounded from below and are thus free of all instabilities.},
doi = {10.1103/PHYSREVD.76.125028},
url = {https://www.osti.gov/biblio/21024093},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 12,
volume = 76,
place = {United States},
year = {2007},
month = {12}
}