Quantum chromodynamics and the soliton model of hadrons

By starting from quantum chromodynamics (QCD) in a finite volume and then taking the infinite-volume limit, we suggest that there is a "phase-transition" phenomenon, which implies the existence of a long-range order in the vacuum for an infinite volume. This long-range order is represented by Lorentz scalars, because of relativistic invariance; such Lorentz scalars can in turn be identified with the phenomenological scalar fields used in a soliton (or bag) model of hadrons. In the phenomenological approach, a permanent quark confinement can be simply viewed as the vacuum of an infinite volume being a perfect "dia-electric" substance, with its dielectric constant $\ensuremath{\kappa}\ensuremath{\rightarrow}0$, while the "vacuum" inside a hadron is normal($\ensuremath{\kappa}=1$), which may be identified as that of QCD for a finite volume. Inside the hadron, exchanges of gauge quanta between quarks give the QCD corrections to the soliton (or bag) model. Spectroscopy of light-quark hadrons is examined by expanding the hadron masses $M$ in powers of the "fine-structure constant" $\ensuremath{\alpha}$ of QCD: $M={M}_{0}+\ensuremath{\alpha}{M}_{1}+{\ensuremath{\alpha}}^{2}{M}_{2}+\ensuremath{\cdots}$. The near-zero mass of the pion is correlated with the existence of a critical value ${\ensuremath{\alpha}}_{c}$ in the mass formula, and the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ anomaly is associated with a large enhancement factor in the $O({\ensuremath{\alpha}}^{2})$ quark-antiquark annihilation diagrams, due to coherence in the various color and flavor degrees of freedom.