Symmetric distributions of bound fermions

Abstract

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.