Abstract
We examine the color-confinement criteria which were proposed by Kugo and Ojima on the basis of the Becchi-Rouet-Stora (BRS) symmetry. With the use of Nakanishi's theorem and the ghost conjugation, we look for the representations of the extended BRS algebra compatible with one of their criteria (the KO condition) and then ask whether or not they are physically acceptable. As a result, the basic BRS cancellation mechanism does not work, and the KO condition is not regarded as a confinement condition.
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