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Title: Generalized Instantaneous Bethe-Salpeter Equation and Exact Quark Propagators


No abstract prepared.

 [1];  [2]
  1. Institute for High Energy Physics, Austrian Academy of Sciences, Nikolsdorfergasse 18, A-1050 Vienna (Austria)
  2. Department of Theoretical Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)
Publication Date:
OSTI Identifier:
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 892; Journal Issue: 1; Conference: QCHS7: 7. conference on quark confinement and the hadron spectrum, Ponta Delgada, Acores (Portugal), 2-7 Sep 2006; Other Information: DOI: 10.1063/1.2714463; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States

Citation Formats

Lucha, Wolfgang, and Schoeberl, Franz F. Generalized Instantaneous Bethe-Salpeter Equation and Exact Quark Propagators. United States: N. p., 2007. Web. doi:10.1063/1.2714463.
Lucha, Wolfgang, & Schoeberl, Franz F. Generalized Instantaneous Bethe-Salpeter Equation and Exact Quark Propagators. United States. doi:10.1063/1.2714463.
Lucha, Wolfgang, and Schoeberl, Franz F. Tue . "Generalized Instantaneous Bethe-Salpeter Equation and Exact Quark Propagators". United States. doi:10.1063/1.2714463.
title = {Generalized Instantaneous Bethe-Salpeter Equation and Exact Quark Propagators},
author = {Lucha, Wolfgang and Schoeberl, Franz F.},
abstractNote = {No abstract prepared.},
doi = {10.1063/1.2714463},
journal = {AIP Conference Proceedings},
number = 1,
volume = 892,
place = {United States},
year = {Tue Feb 27 00:00:00 EST 2007},
month = {Tue Feb 27 00:00:00 EST 2007}
  • 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 solutionsmore » correspond to real discrete spectra bounded from below and are thus free of all instabilities.« less
  • We present a straightforward method to reduce the instantaneous Bethe-Salpeter equation to a set of coupled equations for radial wave functions. In the case of positronium, in particular, the results obtained by Cung {ital et} {ital al}. follow immediately; our procedure is, however, much more general and is intended to be applied to mesonic bound states where competing models need to be tested. We also briefly comment on the numerical solution of the ensuing equations.
  • We present a systematic algebraic and numerical investigation of the instantaneous Beth-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector-types. We explore the stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions for all quark masses.
  • We investigate the light and heavy meson spectra in the context of the instantaneous approximation to the Bethe-Salpeter equation (Salpeter{close_quote}s equation). We use a static kernel consisting of a one-gluon-exchange component and a confining contribution. Salpeter{close_quote}s equation is known to be formally equivalent to a random-phase-approximation equation; as such, it can develop imaginary eigenvalues. Thus our study cannot be complete without first discussing the stability of Salpeter{close_quote}s equation. The stability analysis limits the form of the kernel and reveals that a Lorentz scalar confining interaction in the Salpeter equation leads to instabilities (imaginary eigenvalues), whereas one transforming as the timemore » component of a vector does not. Moreover, the stability analysis sets an upper limit on the size of the one-gluon-exchange component; the value for the critical coupling is determined through a solution of the {open_quote}{open_quote}semirelativistic{close_quote}{close_quote} Coulomb problem. These limits place important constraints on the interaction and suggest that a more sophisticated model is needed to describe the light and heavy quarkonia. {copyright} {ital 1996 The American Physical Society.}« less
  • The Bethe-Salpeter equatton ts solved for general values of the angular momentum, ustng only the ladder approxtmation and the instantaneous interaction approximation. It is first reduced to a set of coupled equations for the singlet and triplet amplitudes, and these are further reduced to the corresponding Schrodinger equations. The non-relativistic potentials are deduced and are found to contain automatically a "core" singularity and spin orbit coupling terms, which are necessary to account for experimental data. The coupling constant, which is the only adjustable parameter, is fitted to the deuteron binding energy, and the potentials are compared with phenomenological potentials. Satisfactorymore » agreement is obtained. (auth)« less