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 analitical calculation system. pacs nombers 11.10.Gh, 04.62.+v 1 Introduction.

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. 1.IntroductionAs well known, not all of the problems of the quantum eld theory are exhausted by the construction of S-matrix. Investigation of evolution of the Universe, behavior of quarks in quantum chromodynamics etc. require the introduction of more general object the so called eective action. Besides that, the program of renormalization of the S-matrix itself has not yet been carried out in terms of the S-matrix alone. Renormalization of the Green functions, therefore, is the central point of the whole theory. Given these functions one can obtain the S-matrix elements with the help of the reduction formulas. In this respect those properties of the generating functionals which remain valid after the transition to the S-matrix is made are of special importance.We mean rst of all the properties of the so called "essential" coupling constants in the sense of S.Weinberg [1]. They are dened as those independent from any redenition of the elds. In the context of the quantum theory one can say that the renormalization of "essential" charges is independent from renormalizations of the elds. Separation of quantities into "essential" and "inessential" ones is convenient and we use it below.In this paper we shall consider the problem of gauge and parametrization dependence of the eective action of R 2 -gravity.There are two general and powerful methods of investigation of gauge dependence in quantum eld theory. The rst of them [2] uses the Batalin-Vilkovisky formalism [3,4,5] and is based on the fact that any change of gauge condition can bepresented

We prove that the β-function of the gauge coupling in 2+1 dimensions gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.

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We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.