skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator reduced Salpeter equation

Abstract

A popular three-dimensional reduction of the Bethe-Salpeter 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 bound-state 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 harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state solutions correspond to real discrete spectra bounded from below and are thus free of all instabilities.

Authors:
; ;  [1]
  1. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 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 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BETHE-SALPETER EQUATION; BOUND STATE; ENERGY SPECTRA; HARMONIC OSCILLATORS; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; STABILITY; THREE-DIMENSIONAL CALCULATIONS; VARIATIONAL METHODS

Citation Formats

Zhifeng, Li, Lucha, Wolfgang, Schoeberl, Franz F, Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna, and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna. Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator 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, A-1050 Vienna, & Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna. Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator 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, A-1050 Vienna, and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna. Sat . "Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator reduced Salpeter equation". United States. https://doi.org/10.1103/PHYSREVD.76.125028.
@article{osti_21024093,
title = {Stability in the instantaneous Bethe-Salpeter formalism: Harmonic-oscillator 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, A-1050 Vienna and Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna},
abstractNote = {A popular three-dimensional reduction of the Bethe-Salpeter 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 bound-state 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 harmonic-oscillator confining interactions. There we are able to prove rigorously that the bound-state 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 = {0556-2821},
number = 12,
volume = 76,
place = {United States},
year = {2007},
month = {12}
}