One-loop effective action for Einstein gravity in special background gauge

Abstract

The one-loop effective action for Einstein gravity in a special oneparameter background gauge is calculated up to first order in a gauge parameter. It is shown that the effective action does not depend upon the gauge parameter on shell.

Basic properties of an alternative flow equation in gravity theories

“…it does not depend on gauges when it is considered on extremals. For the first time the gauge dependence of effective action for gravity theories in the form (2.13) has been described in [23] (for more early descriptions of gauge dependence of effective action in gauge theories see papers [24,25,26,27,28]). This fact allows to state the gauge independence of S-matrix thanks to the equivalence theorem [29].…”

On gauge independence in quantum gravity

“…For the sake of completeness let us verify that on four-sphere S 4 the path integral (20) coincides with the gauge-fixed path integral [24] and with the Hamiltonian path integral [8].…”

“…However, recently some authors [18,19] claimed that due to non-renormalizability of quantum gravity all proofs of gauge-independence are invalid. As far as only the pure Einstein gravity was concerned, their argumentation was based on a single computation by Ichinose [18], which was not supported by independent calculations [20]. According to this point of view, which was expressed in its extreme form in Ref.…”

Gauge and parametrization ambiguity in quantum gravity

“…The general algorithm to explore the gauge-fixing ambiguities in the effective action of gauge theories is wellknown [12] (see also [13] for a simplified one-loop version). And since QG is a particular example of gauge theories, one can easily establish how the effective action depends on the gauge fixing condition at the general level and also for the particular gauge fixing schemes (see, e.g., [14]). At the general level, the issue was elaborated in the paper of Fradkin and Tseytlin devoted mainly to the fourth-derivative models of QG [15] (see also [16] and [17] and finally, [18]).…”