One-loop quantum gravity in a class of covariant gauges

We study methods feasible for the calculation of heat kernel coefficients in one-loop quantum gravity. The thesis begins with a discussion of minimal differential operators and reviews how gauge-fixing leads to minimal operators for the graviton and ghosts. This is followed by an introduction to non-minimal differential operators. We consider the case of Proca field and discuss a reduction technique that allows calculation of heat kernel coefficients arising from non-minimal vector field operators. We show that the same reduction method is not able to tackle the non-minimal operator for a tensor field. This motivates us to apply local momentum space technique for the non-minimal field operator of spin-2 gravity. We verify known results and obtain a new expression for the heat kernel coefficient E1. Finally, we suggest avenues for future research and highlight the significance of non-minimal operators in quantum gravity.