The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

Abstract

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky‐De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman‐Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R2‐gravity. In all these cases the one‐loop Vilkovisky‐De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.

Quantum-induced trans-Planckian energy near horizon

“…Another more serious issue in the perturbative analysis is the long-known gauge-choice dependence. It is a more fundamental question[57][58][59].…”

Exact renormalization group and running Newtonian coupling in higher-derivative gravity

“…Note that K = 3f 2 f 2 +2ν 2 what corresponds to the choice of so-called gaugefixing independent effective action (for a review see [1,11]). By this choice, we solve the gauge-dependence problem (for a related discussion in case of Einstein gravity, see [7]).…”

Gauge dependence and a new kind of two-dimensional gravity theory with trivial quantum corrections

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