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 TMF, 2004, Volume 140, Number 2, Pages 241–255 (Mi tmf96)

Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature

Yu. V. Pavlov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We consider a scalar field with a Gauss–Bonnet-type coupling to the curvature in a curved space-time. For such a quadratic coupling to the curvature, the metric energy-momentum tensor does not contain derivatives of the metric of orders greater than two. We obtain the metric energy-momentum tensor and find the geometric structure of the first three counterterms to the vacuum averages of the energy-momentum tensors for an arbitrary background metric of an $N$-dimensional space-time. In a homogeneous isotropic space, we obtain the first three counterterms of the $n$-wave procedure, which allow calculating the renormalized values of the vacuum averages of the energy-momentum tensors in the dimensions $N=4,5$. Using dimensional regularization, we establish that the geometric structures of the counterterms in the $n$-wave procedure coincide with those in the effective action method.

Keywords: scalar field, quantum theory in curved space, renormalization, dimensional regularization

DOI: https://doi.org/10.4213/tmf96

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English version:
Theoretical and Mathematical Physics, 2004, 140:2, 1095–1108

Bibliographic databases:

Citation: Yu. V. Pavlov, “Renormalization and Dimensional Regularization for a Scalar Field with Gauss–Bonnet-Type Coupling to Curvature”, TMF, 140:2 (2004), 241–255; Theoret. and Math. Phys., 140:2 (2004), 1095–1108

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf96
• https://doi.org/10.4213/tmf96
• http://mi.mathnet.ru/eng/tmf/v140/i2/p241

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Grib A.A., Pavlov Yu.V., “Quantum field theory in curved spacetime and the dark matter problem”, XXVI Workshop on Geometrical Methods in Physics, AIP Conference Proceedings, 956, 2007, 96–106
2. Grib, AA, “Is Dark Matter the Relic of the Primordial Matter That Created the Visible Matter of the Universe?”, Gravitation & Cosmology, 14:1 (2008), 1
3. Pavlov, YV, “Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field”, Gravitation & Cosmology, 14:4 (2008), 314
4. Haouat S., Chekireb R., “On the Creation of Scalar Particles in a Flat Robertson-Walker Spacetime”, Modern Phys Lett A, 26:35 (2011), 2639–2651
5. Yu. V. Pavlov, “Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models”, Theoret. and Math. Phys., 174:3 (2013), 438–445
6. Pavlov Yu.V., “On Creation of Scalar Particles With Gauss-Bonnet Type Coupling To Curvature in Friedmann Cosmological Models”, Gravit. Cosmol., 20:1 (2014), 21–25
7. Grib A.A. Pavlov Yu.V., “Particle creation in the early Universe: Achievements and problems”, Gravit. Cosmol., 22:2 (2016), 107–115
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