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We discuss a confining model for charmonium in which the attractive force arederived from a new type of gauge field equation with a generalized $SU_3$ gaugesymmetry. The new gauge transformations involve non-integrable phase factorswith vector gauge functions $\om^a_{\mu}(x)$. These transformations reduce tothe usual $SU_3$ gauge transformations in the special case $\om^a_\mu(x) =\p_\mu \xi^a(x)$. Such a generalized gauge symmetry leads to the fourth-orderequations for new gauge fields and to the linear confining potentials. Thefourth-order field equation implies that the corresponding massless gauge bosonhas non-definite energy. However, the new gauge boson is permanently confinedin a quark system by the linear potential. We use the empirical potentials ofthe Cornell group for charmonium to obtain the coupling strength $f^2/(4\pi)\approx 0.19$ for the strong interaction. Such a confining model of quarkdynamics could be compatible with perturbation. The model can be applied toother quark-antiquark systems.

A Confining Model for Charmonium and New Gauge Invariant Field Equations