
Physics 1993
QCD Originated Dynamical Symmetry for HadronsAbstract: We extend previous work on the IR regime approximation of QCD in which the dominant contribution comes from a dressed twogluon effective metriclike field $G_{\mu\nu} = g_{ab} B^{a}_{\mu} B^{b}_{\nu}$ ($g_{ab}$ a color SU(3) metric). The ensuring effective theory is represented by a pseudodiffeomorphisms gauge theory. The second quantized $G_{\mu\nu}$ field, together with the Lorentz generators close on the $\bar{SL}(4,R)$ algebra. This algebra represents a spectrum generating algebra for the set of hadron states of a given flavor  hadronic "manifields" transforming w.r.t. $\bar{SL}(4,R)$ (infinitedimensional) unitary irreducible representations. The equations of motion for the effective pseudogravity are derived from a quadratic action describing Riemannian pseudogravity in the presence of shear ($\bar{SL}(4,R)$ covariant) hadronic matter currents. These equations yield $p^{4}$ propagators, i.e. a linearly rising confining potential $H(r) \sim r$, as well as linear $J \sim m^{2}$ Regge trajectories. The $\bar{SL}(4,R)$ symmetry based dynamical theory for the QCD IR region is applied to hadron resonances. All presently known meson and baryon resonances are successfully accommodated and various missing states predicted. (Lectures presented at the Danube Workshop '93, June 1993, Belgrade, Yugoslavia.)
