โ Scribed by Kurt Just
No coin nor oath required. For personal study only.
Relativistic models of hadrons composed of the simplest kind of Fermi quarks will be described in subsequent papers by symmetric wavefunctions S, which vanish when all the relative positions of the constituents are spacelike. These S are highly preferable, not in spite of, but thanks to the usual connection of spin and statistics. The principles of the new models are explained in comparison with other quark and parton models. If needed at all, the Bethe-Salpeter amplitude T of a bound state can be obtained from its symmetric distribution S by a "dispersion" integral. An extension to three constituents will be given later. It is precisely because S vanishes for spacelike internal separations that practical estimates for strongly bound states will more readily employ that symmetric distribution than the time ordered T. Field theory and its description of bound states as well as properties and interactions of hadrons are invoked for completeness and the benefit of specialists. Only elementary notions from such topics, however, are needed for the main conclusion. It says that the simplest Fermi quarks (without any "hidden" quantum number) offer the best explanation for the widely accepted symmetry of their wavefunctions in baryons. The failure to observe quarks and also their oscillator shaped interaction within hadrons will later be connected with the same simplicity and a vanishing mass of "bare" quarks.
[3]. To the author's knowledge, however, this approach has not been considered for the Bethe-Salpeter amplitudes T of bound states. The reasons may be that their "absorptive" parts do not enter an "optical" theorem and that no simple equation for them has been known.
The equation suggested here will be obtained from the Bethe-Salpeter equation and also from a phenomenological Dirac equation. Both of these derivations are heuristic, but the result need not be worse than the ladder approximation to the Bethe-Salpeter equation. In any case, the new approach will yield more convenient approximations, especially for strongly bound states with interactions 232
๐ SIMILAR VOLUMES
The bound states of spin 4 and spin zero particles in the field of a point SU((2) dyon are studied for isospinor and isovector representations. Energy levels and eigenfunctions for all angular momenta have been calculated for isospinor fermions, isospinor bosons, and isovector bosons. For isovector