Bethe-Salpeter Equations with Instantaneous Confinement: Establishing Stability of Bound States

Details Bethe-Salpeter Equations with Instantaneous Confinement: Establishing Stability of Bound States Bethe-Salpeter Equations with Instantaneous Confinement: Establishing Stability of Bound States

2010-08-08

arxiv.org/abs/1008.1404v1

AIP Conf.Proc.1317:122-127,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

6 pages, contributed to QCD@Work 2010 - International Workshop on Quantum Chromodynamics: Theory and Experiment (20 - 23 June

Scientific paper

10.1063/1.3536544

Salpeter equations with potential functions rising to infinity in configuration space do not automatically predict stable bound states. For this to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is crucial. At least for interaction potentials of harmonic-oscillator form analytic scrutinies of Salpeter equations with confining interactions may identify those Bethe-Salpeter kernels which describe bound states free from the notorious instabilities encountered in numerical evaluations. Such truly confining kernels can be singled out systematically by requesting the resulting bound-state energy spectra to be both real and discrete.

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