Symmetry breaking quasi-particle method for baryons and for quarks I. Bound state problem

Abstract

The quasi-particle method (essentially a non-perturbational approximation of quantum field theory) is applied to an SU 3 symmetric four-fermion interaction between octet-baryons N and antibaryons N (of between quarks and antiquarks). The method is developed in such a way, that the physical particles and resonances themselves appear as quasi-particles in a bound state approximation. The main weight is attached to the understanding of the principles of the method. The individual quasi-particle operators obtained are of the form Ω = u N + ν N ∗ . Their eigenvalue spectrum is compared with the observed baryon resonances. Spontaneous dynamical breaking of SU 3 symmetry appears and leads primarily to a GMO formula for the gap constants, irrespective of the coupling strength. (Similar results are obtained for quarks.) The GMO formula for the baryon masses is obtained in the strong coupling limit. (Furthermore mass formulae for quarks are derived.) Further it is shown in detail that the origin of the symmetry breaking is the fact that the quasi-particle method is an averaging approximation. Quasi-particles of higher order are considered in a preliminary way. Especially the meson spectra are treated in the lowest approximation. It is shown, that the first two of the three typical difficulties of the quasi-particle approximation [(i) inequivalent representations and degenerate vacua, (ii) parity mixed vacuum and (iii) spurious states ≡ Goldstone mesons) are avoided by our bound state approximation. The method is applicable to all compact symmetry groups.