The generalized Schwinger-DeWitt technique and the unique effective action in quantum gravity

The purpose of this talk is to discuss how one can define and compute the effective action. The authors consider the following subjects: 1. The parameterization-independent and gauge-independent definition of the effective action in QFT. 2. Extension of the Schwinger-DeWitt technique to nonminimal operators, higher-order operators and higher loop orders. The method of generating functional traces. 3. Summation of the proper-time series. Nonlocal terms in the effective action. 4. Applications. The complete algorithm for divergences of a fourth-order operator. The calculational technique for the unique effective action in gauge theories. The unique counterterms for Einstein's theory. Covariant calculation of divergences in two-loop graphs and the absence of leading divergences in two-loop quantum gravity