Analytic Quest for Confining Interaction Kernels in Instantaneous Bethe-Salpeter Equations
arXiv:1010.0866 · doi:10.1063/1.3575121
Abstract
The Salpeter equation, a standard tool in hadron physics, constitutes a well-defined three-dimensional approximation to the Bethe-Salpeter formalism for the description of bound states within quantum field theories. However, if confinement is implemented in a too careless manner, the Salpeter equation might predict unstable states where only truly bound states are expected. A systematic spectral analysis of the Salpeter equation might serve to single out those Bethe-Salpeter interaction kernels which indeed yield stable bound states, with associated energy eigenvalues belonging to a real discrete spectrum bounded from below.
contributed to Quark Confinement and the Hadron Spectrum IX - QCHS IX (30 August - 3 September 2010, Madrid, Spain), to appear in the proceedings