Can quarks always be confined by a linear potential?

It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r ₀)^a orln(r/r ₀]^a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.