Covariant perturbation theory (II). Second order in the curvature. General algorithms

Barvinsky, A. O.; Vilkovisky, G. A.

doi:10.1016/0550-3213(90)90047-h

Cited by 337 publications

(597 citation statements)

References 14 publications

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“…The expression for the conformal anomaly (10) has been used to get an explicit form of the anomaly-induced action in the scalar-metric theory (cosmon model) [20], with very interesting phenomenological implications. In next sections we will show that the approach described above agrees with the calculation based on the heat-kernel [12] and Pauli-Villars methods.…”

Section: Local Conformal Symmetry and Dimensional Regularizationmentioning

confidence: 58%

“…Alternatively one can apply the proper-time cut-off regularization [7,12] here, the result is of course the same. Later on we shall see that if instead of dimensional regularization we use the covariant Pauli-Villars regularization [7] the logarithmic divergent part of the action will agree with (14).…”

Section: Self-interacting Scalar Fieldmentioning

confidence: 99%

“…The calculation of both divergent and finite part of the effective action has been performed up to the second order in the curvatures (R µναβ ,P ) using Feynman diagrams on flat backgrounds and also the heat kernel solution [12,13]. The result is [14,15] …”

Section: Self-interacting Scalar Fieldmentioning

confidence: 99%

“…Furthermore, we use Barvinsky-Vilkovisky formalism [12,13] and the approach developed in [14] to derive the non-local finite part of the effective action for the case of massive Yukawa model. In the case of self-interacting scalar theory, this calculation has been already done in [15].…”

Section: Introductionmentioning

confidence: 99%

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Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

2006

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We analyze the problem of the existing ambiguities in the conformal anomaly in theories with external scalar field in curved backgrounds. In particular, we consider the anomaly of self-interacting massive scalar field theory and of Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of a local non-minimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise.

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Section: Local Conformal Symmetry and Dimensional Regularizationmentioning

confidence: 58%

Section: Self-interacting Scalar Fieldmentioning

confidence: 99%

Section: Self-interacting Scalar Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

2006

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“…Ref. [22], an idea that was put at work by Gusev and Zelnikov [23] to compute the effective action in dilatonic two-dimensional gravity. Recall that effective actions are related to determinants of elliptic PDO, susceptible of being regularized by means of the derivative of the spectral zeta function at the origin of the s-complex plane.…”

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confidence: 99%

Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

2016

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Spectral heat kernel/zeta function regularization procedures are employed in this paper to control the divergences arising from vacuum fluctuations of Bogomolnyi-Prasad-Sommerfield vortices in the Abelian Higgs model. Zero modes of vortex fluctuations are the source of difficulties appearing when the standard Gilkey-de Witt expansion is the tool used in the calculations of one-loop shifts of vortex masses and string tensions. A modified GdW expansion is developed to diminish the impact of the infrared divergences due to the vortex zero modes of fluctuation. With this new technique at our disposal we compute the one-loop vortex mass shifts in the planar AHM and the quantum corrections to the string tension of the magnetic flux tubes living in three dimensions. In both cases it is observed that weak repulsive forces surge between these classically noninteracting topological defects caused by vacuum quantum fluctuations.

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Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

Kummer

Vassilevich

1999

Annalen der Physik

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Hawking radiation in d = 4 is regarded as a well understood quantum theoretical feature of Black Holes or of other geometric backgrounds with an event horizon. On the other hand, the dilaton theory, emerging after spherical reduction, and generalized dilaton theories only during the last years became the subject of numerous studies which unveiled a surprisingly difficult situation. Recently we have found some solution to the problem of Hawking flux in spherically reduced gravity which has the merit of using a minimal input. It leads to exact cancellation of negative contributions to this radiative flux, encountered in other approaches at infinity, so that our result asymptotically coincides with the one of minimally coupled scalars. The use of an integrated action is avoided — although we have been able to present also that quantity in a closed expression. This short review also summarizes and critically discusses recent activities in this field, including the problem of “conformal frames” for the background and questions which seem to be open in our own approach as well as in others.

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Covariant perturbation theory (II). Second order in the curvature. General algorithms

Cited by 337 publications

References 14 publications

Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds

Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

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