Preface

Quark-model study of few-baryon systems

“…Historically the first model of hadron structure, a non-relativistic quark model, appeared in the nineteen sixties right after Gell-Mann and Zweig [11,12] introduced the quarks as the members of the triplet representation of SU (3) F lavour from which the hadron representations could be constructed. The lack of observation of free quarks in nature seemed to indicate their strong binding inside hadrons.…”

Quark confinement and curved spaces

“…In the nonrelativistic oscillator model [5]- [7], the Hamiltonian (1) leads to confining oscillator-type wave functions that contain a factor e −β(r , where β is a constant. In [17] with the potential (4), the approximate behavior of the wave function is ψ ∝ Φ(r)e −βr 2 and in the Cornell model [9], where the potential of the type (2) is used, a similar behavior occurs. In the Bogolioubov and in the MIT bag models that consider a potential of the type (3), the wave functions contain a factor e −β √ m 2 −E 2 (r−r0) , and quark confinement appears in the limit V 0 → ∞, where the wave function is constant for r = R and 0 for r > R.…”

“…The introduction of quarks in the physical theory in 1964, by the Gell-Mann [1] and Zweig [2] hypothesis, has also introduced the annoying question of quark confinement. If by one hand this theory was able to organize and to explain the main proprieties of the hadrons with the scheme called the eightfold way [3], on the other hand, the impossibility of observing free quarks could be considered as a major problem.…”

MAXIMALLY SYMMETRIC MINIMAL UNIFICATION MODEL SO(32) WITH THREE FAMILIES IN TEN-DIMENSIONAL SPACETIME

“…The electromagnetic interaction is well described by an U(1) gauge symmetry, and the weak interaction is characterized by a left-handed SU(2) L gauge symmetry based on the parity violation [4]. The strong interaction of quarks [5,6] described by the Yang-Mills gauge theory [7] with a gauge symmetry SU(3) C displays a behavior of asymptotic freedom [8,9]. Three families of quarks and leptons are necessary for a non-trivial CP-violating phase [10], which can be originated from spontaneous CP violation [11,12,13].…”