Stability in the instantaneous Bethe-Salpeter formalism: reduced exact-propagator bound-state equation with harmonic interaction

Abstract

Several numerical investigations of the Salpeter equation with static confining interactions of Lorentz-scalar type revealed that its solutions are plagued by instabilities of presumably Klein-paradox nature. By proving rigorously that the energies of all predicted bound states are part of real, entirely discrete spectra bounded from below, these instabilities are shown, for confining interactions of harmonic-oscillator shape, to be absent for a reduced version of an instantaneous Bethe-Salpeter formalism designed to generalize the Salpeter equation towards an approximate inclusion of the exact propagators of all bound-state constituents.

13 pages

References in corpus (10)

• On the instantaneous Bethe-Salpeter equation
• On the Lorentz structure of the confinement potential
• Instantaneous Bethe-Salpeter equation: improved analytical solution
• Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
• On the validity of the reduced Salpeter equation
• Instantaneous Bethe-Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound-State Constituents
• Stability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy
• Instantaneous Bethe-Salpeter equation: utmost analytic approach
• The stability of the spectator, Dirac, and Salpeter equations for mesons
• Exact-propagator instantaneous Bethe-Salpeter equation for quark-antiquark bound states

Cited by in corpus (4)

• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• Instantaneous Bethe-Salpeter Kernel for the Lightest Pseudoscalar Mesons
• A semirelativistic treatment of spinless particles subject to the Yukawa potential with arbitrary angular momenta
• A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential