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

Journal Article · Sat Dec 15 04:00:00 EST 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.125028· OSTI ID:21024093

Zhifeng, Li; Lucha, Wolfgang; Schoeberl, Franz F ^[1]

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1. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)

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.

• OSTI ID: 21024093
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 76; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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