Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-07-23
Phys.Rev.D76:125028,2007
Physics
High Energy Physics
High Energy Physics - Phenomenology
23 pages, 3 figures, extended conclusions, version to appear in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.76.125028
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 this 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 energy spectra bounded from below and are thus free of any instabilities.
Li Zhi-Fang
Lucha Wolfgang
Sch"oberl Franz F.
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