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The form of the resulting Feynman propagators in a proposed local and gaugeinvariant QCD for massive fermions suggests the existence of indefinite metricassociated to quark states, a property that might relate it with the knownLee-Wick theories. Thus, the nature of the asymptotic free quark states in thetheory is investigated here by quantizing the quadratic part of the quarkaction. As opposite to the case in the standard QCD, the free theory does notshow Hamiltonian constraints. The propagation modes include a family ofmassless waves and a complementary set of massive oscillations. The theory canbe quantized in a way that the massive modes show positive metric and themassless ones exhibit negative norms. It is remarked that, since QCD isexpected to not exhibit gluon or quark asymptotic states, the presence ofnegative metric massless modes does not constitute a definite drawback of thetheory. In addition, the fact that the positive metric quark states aremassive, seems to be a good feature of the model, being consistent with theapproximate existence of asymptotically free massive states in high energyprocesses.

On the metric of the space of states in a modified QCD