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The one-loop ultraviolet divergences of the quantized coupled Einstein-Yang-Mills fields are evaluated. They are precisely of the same nonrenormalizable form as for a corresponding set of free Maxwell fields together with the usual flat-space Yang-Mills divergences. The two free Yang-Mills field parameters, namely the group dimension and the self-coupling constant, cannot be chosen to make the one-loop divergences renormalizable in the usual sense.
Deser et al. (Fri,) studied this question.
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