All one-loop divergences of the quantized Einstein-Maxwell system are calculated, using dimensional regularization and the background-field method. The resulting counterterms, including photon and graviton ghost contributions, are quadratic in curvatures when evaluated on the mass shell, and cannot be renormalized away by rescaling. Brans-Dicke theory is also nonrenormalizable; source-free Einstein theory with cosmological term is (formally) renormalizable, as are Weyl models.
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Deser et al. (1974) studied this question.
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