One-loop counterterms for the dimensional regularization of arbitrary Lagrangians

Pronin, P. I.; Stepanyantz, K. V.

doi:10.1016/s0550-3213(96)00646-3

Cited by 26 publications

(61 citation statements)

References 14 publications

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“…; ; K ; L ; Y ] C C T h ; (16) W i lnZ; h = W kT ; C = W ; C = W (17) and noting that d~ d = dW d ; (18) we rewrite (14) as the Slavnov identity for~…”

Section: Slavnov Identitiesmentioning

confidence: 99%

“…According to algorithm derived in [17] we should rst calculate the part of 2 Then we substitute r ! n ; n being a vector with n 2 = 1, and calculate the "propagator" (K n 1 ) ; which is the inverse of the operator (K n ) ; = 2 S gf hh : (K n ) ; (K n 1 ) ; = ; (K n 1 ) ; = 1 = 2(g g +g g ) + A 1 g g +B 1 (g n n +g n n +g n n + g n n ) + C 1 ( g n n + g n n ) + D 1 n n n n ; where …”

Section: Appendix Amentioning

confidence: 99%

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Gauge and parametrization dependence in higher derivative quantum gravity

Kazakov

Pronin

1999

Phys. Rev. D

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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

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“…; ; K ; L ; Y ] C C T h ; (16) W i lnZ; h = W kT ; C = W ; C = W (17) and noting that d~ d = dW d ; (18) we rewrite (14) as the Slavnov identity for~…”

Section: Slavnov Identitiesmentioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

Gauge and parametrization dependence in higher derivative quantum gravity

Kazakov

Pronin

1999

Phys. Rev. D

Self Cite

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“…[25] for the pure Yang-Mills theory taking as mass regulator M i = M |i| and µ j = µ|j| ∀i, j. We think that it can be extended to include the matter taking m f k = m|k| for k = 0 and even to the background field formalism using the tools developed in [26]. The higher covariant derivatives complicate the Feynman rules and hence make the above proofs a difficult task.…”

Section: Regularized Gauge Invariant Effective Actionmentioning

confidence: 99%

Non-diagrammatic calculation of QCD one-loop β-function based on the renormalization group equation

Chiantese¹

2001

J. High Energy Phys.

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Using the higher covariant derivatives regularization of gauge theories in the framework of the background field method, supplemented with one-loop Pauli-Villars regulator fields, we obtain a version of the renormalization group equation for the regulator fields, whose vacuum energy depends on the background gauge field. It is evaluated using an anomalous Ward-Takahashi identity, which is related to the rescaling anomaly of the auxiliary fields, obtained by the Fujikawa approach. In this way the anomalous origin of the one-loop β-function in QCD is clearly shown in terms of scaling of effective Lagrangians without the use of any Feynman diagram. The simplicity of the method is due to the preservation of the background and quantum gauge invariance in any step of the calculation.

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“…From the other side, the total derivative terms were not found in Ref. [2]. (Their contributions to the one-loop divergences are integrals of total derivatives.)…”

Section: Introductionmentioning

confidence: 97%

“…Therefore, there is a problem how the results of Ref. [2] can be generalized in order to take into account total derivative terms. These contributions are essential in some cases, for example, if the calculations are made on the (anti) de-Sitter background.…”

Section: Introductionmentioning

confidence: 99%

Equation for one-loop divergences in two dimensions and its application to higher-spin fields

Попова

Stepanyantz

2016

Theor Math Phys

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A simple formula for one-loop logarithmic divergences on the background of a twodimensional curved space-time is derived for theories for which the second variation of the action is a nonminimal second order operator with small nonminimal terms. In particular, this formula allows to calculate terms which are integrals of total derivatives. As an application of the result, one-loop divergences for the higher spin fields on the constant curvature background are obtained in a nonminimal gauge, which depends on two parameters. By an explicit calculation we demonstrate that with the considered accuracy the result is gauge independent. Moreover, the result appeared to be independent of the spin s for s ≥ 3.

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One-loop counterterms for the dimensional regularization of arbitrary Lagrangians

Cited by 26 publications

References 14 publications

Gauge and parametrization dependence in higher derivative quantum gravity

Gauge and parametrization dependence in higher derivative quantum gravity

Non-diagrammatic calculation of QCD one-loop β-function based on the renormalization group equation

Equation for one-loop divergences in two dimensions and its application to higher-spin fields

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