Extended gauge theory and its mass spectrum

Abstract

Based on the recently proposed restricted gauge theory an extended gauge theory is constructed which takes into account not only the local structure but also the topological structure of a non-Abelian gauge symmetry into its dynamics. The gauge potential is made of two parts, the binding gluons which provide the color-confining force and the valence gluons which behave as a gauge-covariant colored vector source. The physical spectrum of the theory includes the magnetic glueballs which are the massive collective modes of the vacuum condensation, and the electric glueballs made of the valence gluons which form a set of linearly rising trajectories of their own. Based on the group SU(2) the slope parameter ${{\ensuremath{\alpha}}^{\ensuremath{'}}}_{X}$ of the leading glueball trajectories is estimated to be ${{\ensuremath{\alpha}}^{\ensuremath{'}}}_{X}\ensuremath{\simeq}0.47{\ensuremath{\alpha}}^{\ensuremath{'}}$ (${\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\simeq}0.9$ ${\mathrm{GeV}}^{2}$ is the Regge slope parameter of the mesons). Also, a crude estimate of the typical mass scale of the ground states of the trajectories is presented.