Abstract
In the first part of this paper the U(1) problem of Crewther is reanalyzed. It is argued that certain essential constraints amount to a demand for terms in which different, but integral, topological charges are associated with the different quark flavors. Conventional QCD cannot meet this demand. In the second part a multiple-field generalization of QCD is presented. Its use is illustrated in the derivation of an expression for the vacuum expectation value of a general function of the quark fields. In the third part we show that the new chromodynamics preserves the QCD perturbation theory, and solves the U(1) problem. We examine the $\ensuremath{\theta}$ dependence of the amplitudes and comment on the implications for current algebra.
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