One-loop counterterms for the dimensional regularization of arbitrary Lagrangians

We present master formulas for the divergent part of the one-loop effective action for an arbitrary (both minimal and nonminimal) operators of any order in the 4-dimensional curved space. They can be considered as computer algorithms, because the one-loop calculations are then reduced to the simplest algebraic operations. Some test applications are considered by REDUCE analytical calculation system.Comment: 39 pages, Latex, 3 PS figures, replaced with published versio

Gauge and parametrization dependence in higher derivative quantum gravity

The structure of counterterms in higher derivative quantum gravity is reexamined. Nontrivial dependence of charges on the gauge and parametrization is established. Explicit calculations of two-loop contributions are carried out with the help of the generalized renormgroup method demonstrating consistency of the results obtained.Comment: 22 pages, Latex, no figure

Gauge dependence of effective gravitational field

The problem of gauge independent definition of effective gravitational field is considered from the point of view of the process of measurement. Under assumption that dynamics of the measuring apparatus can be described by the ordinary classical action, effective Slavnov identities for the generating functionals of Green functions corresponding to a system of arbitrary gravitational field measured by means of scalar particles are obtained. With the help of these identities, the total gauge dependence of the non-local part of the one-loop effective apparatus action, describing the long-range quantum corrections, is calculated. The value of effective gravitational field inferred from the effective apparatus action is found to be gauge-dependent. A probable explanation of this result, referring to a peculiarity of the gravitational interaction, is given.Comment: Revised version as publishe