On the Lorentz structure of the confinement potential

Preprint

10 February 1994

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.nucl-th/9402019

Abstract

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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All Related Versions

Version 1, 1994-02-10, ArXiv
Published version: Nuclear Physics A, 585 (4), 705.

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