Abstract
We show from action integral that under the assumption of
longitudinal dominance and transverse confinement, QCD4 in (3+1)
dimensional space-time can be approximately compactified into QCD2
in (1+1) dimensional space-time. In such a process, we find the
relation between the coupling constant g(2D) in QCD2 and the
coupling constant g(4D) in QCD4. We show how the quark and the
gluon in QCD2 acquire masses arising their being confined within
the tube, and how all these quantities depend on the excitation of
the partons in the transverse degree of freedom. The variation of
the gluon fields leads to an additional mass that depends on the
coupling constant g(2D). The compactification facilitates the
investigation of some problems in QCD4 in the simpler dynamics of
QCD2.
