ABSTRACT
The standard effective action is the generating functional of vertex functions and therefore it must depend on the parametrization of the quantum fields. In gauge theories it leads to dependence of the effective action on the choice of gauge conditions which are used for quantization. From the geometric point of view, this gauge dependence of the standard effective action is due to the fact that the functional integral for effective action depends on the parametrization of the space of group orbits. The chapter discusses the relation of the one-loop unique effective action to the standard one. The unique effective action is gauge invariant and gauge fixing independent. The calculation of the unique effective action in quantum gravity with the metric leads to an explicit α-dependence of the unique effective action.
