The ultraviolet behavior of Einstein gravity

We have recently reported on a two-loop calculation showing that the S matrix of Einstein's theory of gravity contains non-renormalizable ultraviolet divergences in four dimensions. In this paper we present several details of the work. We discuss the calculation both in background field and in normal field theory, and we describe a method for eliminating ghost fields in gauge theories by embedding them in suitable extensions of the gauge fields à la Kaluza-Klein.