The first part of a detailed analysis of the one-loop divergences of fourth-order gravity theories is presented. The functional-integral structure is determined and the three kinds of ghosts which appear are discussed. Field operators and gauge-fixing terms are derived and are found to be far more complicated than those of standard second-order theory, whose details are presented for comparison to the fourth-order case. We outline how, in future papers, we will approach the computation of the one-loop counterterms using pseudo-differential operator techniques and related methods. We also discuss briefly what other workers have done and are doing in studies of the problems inherent in fourth-order gravity and its extensions. Finally, we emphasize the need to investigate the full non-linear theory with coordinate-space methods and mention some of the problems brought about by linearization. Details of calculations and the multilevel-mass-spectrum theory are presented in several appendices.

• Received 29 April 1983

DOI:https://doi.org/10.1103/PhysRevD.28.1876