Abstract
We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized SU
3
gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions
ω
ω
a
(
x
). These transformations reduce to the usual SU
3
gauge transformations in the special case
ω
μ
a
(
x
) = ∂
μ
ξ
a
(
x
). Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength
f
2
/(4
π
) ≈ 0.19 for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems.