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One-Loop Effective Action: Nonlocal Form Factors and Renormalization Group

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Abstract

We review and present full details of the Feynman diagram based and the heat-kernel method based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field. The paper has pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject. The functional calculations are based on the solution by Avramidi and Barvinsky and Vilkovisky for the heat kernel and are performed in curved space-time. One of the important points is that the main structure of nonlocalities is the same as in the flat background.

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Notes

  1. There was also an earlier calculation of the gravitational form factors with temperature [18], but without an analysis of decoupling.

  2. Indeed, there are finite nonlocal surface terms related to \(a_{1}\), and these are regularization-independent. One can learn about this aspect in [4, 13].

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Funding

This work of I.Sh. was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq under the grant 303635/2018-5 and Fundaзão de Amparo à Pesquisa de Minas Gerais—FAPEMIG under the project APQ-01205-16.

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  1. Departamento de Física, ICE, Universidade Federal de Juiz de Fora, Campus Universitário, Juiz de Fora, 36036-330, MG, Brazil

    Poliane de Morais Teixeira, Ilya L. Shapiro & Tiago G. Ribeiro

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  1. Poliane de Morais Teixeira
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Correspondence to Poliane de Morais Teixeira, Ilya L. Shapiro or Tiago G. Ribeiro.

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Teixeira, P.d., Shapiro, I.L. & Ribeiro, T.G. One-Loop Effective Action: Nonlocal Form Factors and Renormalization Group. Gravit. Cosmol. 26, 185–199 (2020). https://doi.org/10.1134/S0202289320030123

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