On the Lorentz structure of the confinement potential

Details On the Lorentz structure of the confinement potential On the Lorentz structure of the confinement potential

1994-02-10

arxiv.org/abs/nucl-th/9402019v1

Nucl.Phys. A585 (1995) 705-726

Physics

Nuclear Physics

Nuclear Theory

18 pages using RevTeX 3.0, with 8 figures available upon request, FSU-SCRI-94-15

Scientific paper

10.1016/0375-9474(94)00722-Y

We investigate the Lorentz structure of the confinement potential through a study of the meson spectrum using Salpeter's instantaneous approximation to the Bethe-Salpeter equation. The equivalence between Salpeter's and a random-phase-approximation (RPA) equation enables one to employ the same techniques developed by Thouless, in his study of nuclear collective excitations, to test the stability of the solutions. The stablity analysis reveals the existence of imaginary eigenvalues for a confining potential that transforms as a Lorentz scalar. Moreover, we argue that the instability persists even for very large values of the constituent quark mass. In contrast, we find no evidence of imaginary eigenvalues for a timelike vector potential --- even for very small values of the constituent mass.

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