Unique effective action in five-dimensional Kaluza-Klein theory

The problem of gauge and parametrization dependence in self-consistent dimensional reduction of five-dimensional quantum gravity is discussed. It is shown how the modification of the background-field method suggested by Vilkovisky is crucial for obtaining the correct result. We find that there are no physically acceptable self-consistent solutions of the form ${\mathrm{R}}^4$×${\mathrm{S}}^1$ at the one-loop level.