If we assume that the strong interactions of baryons
and mesons are correctly described in terms of
the broken "eightfold way", we are tempted to
look for some fundamental explanation of the situation.
A highly promised approach is the purely dynamical
"bootstrap" model for all the strongly interacting
particles within which one may try to derive
isotopic spin and strangeness conservation and
broken eightfold symmetry from self-consistency
alone. Of course, with only strong interactions,
the orientation of the asymmetry in the unitary
space cannot be specified; one hopes that in some
way the selection of specific components of the F-spin
by electromagnetism and the weak interactions
determines the choice of isotopic spin and hypercharge
directions.

A Schematic Model of Baryons and Mesons

Quark dynamics and strong meson decays

Simple and straightforward procedures are developed for deriving complete large coupling expansions for the wavefunctions, eigenenergies, and Regge trajectories of the generalized Yukawa potential. The procedures may easily be applied to similar problems.

Large coupling expansions for eigenenergies and Regge trajectories of the Yukawa potential

Bethe-Salpeter equation and current conservation

Relativistic three-particle problem and heavy quarks

The dynamics of strong binding of heavy scalar particles (quarks) are discussed with the help of the Bethe-Salpeter equation with a smooth ladder-type kernel. For this purpose, the Bethe-Salpeter amplitudes are expanded intoO4 spherical functions and the remaining « hyper-radial » equation is solved by a variational method. These calculations are considered as a model of mesons as bound states of heavy quarks. The low-lying mesons form linear trajectories with a slope of 1 (GeV)−2. The modification of the vector-meson dominance form factor by the bound-state wave functions is calculated and found to be in good agreement with experiment.

Relativistic scalar quark model with strong binding

In our lectures we deal with the specific dynamical problems arising in the formulation of the relativistic quark model in the framework of field theory1. After the discussion of some basic questions occurring in this particular attempt towards a foundation of hadron dynamics, we develop extensively the methods for the description of mesons as quark-antiquark bound-states and give some illuminating phenomenological applications. In order to outline the spirit of our approach, let us first answer some general questions.

M. Krammer

Papers

Relativistic scalar quark model with strong binding

Dynamical Problems of the Relativistic Quark Model