Derivation of a Quark Confinement Potential from QCD

A quark confinement potential is derived from QCD Lagrangial under the two assumptions in the energy region relevant to quark confinement. The possibility of perturbation in QCD is assumed, and the momentum of the gluon transfered by the quark is larger than the mass of the internal quark, so that the expansion of ${m^2 /{q^2}}$ is assumed to be reliable. This potential comes from the one loop diagrams in the expansion of $m^2 /{q^2}$, especially here, the vacuum polarization diagram is examined. This explains the quark confinement mechanism on the basis of QCD and the Regge trajectories which is governed by a linear potential.