Pla, S. orcid.org/0000-0001-8286-8118 and Winstanley, E. orcid.org/0000-0001-8964-8142 (2023) Equivalence of the adiabatic expansion and Hadamard renormalization for a charged scalar field. Physical Review D, 107 (2). 025004. ISSN 2470-0010
Abstract
We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger, and adiabatic) to the renormalization of expectation values of field operators acting on a charged quantum scalar field. First, we demonstrate that the DeWitt-Schwinger representation of the Feynman Green’s function is a particular case of the Hadamard representation. Next, we restrict attention to a spatially flat Friedmann-Lemaître-Robertson-Walker universe with time-dependent, purely electric, background electromagnetic field, considering two-, three-, and four-dimensional space-times. Working to the order required for the renormalization of the stress-energy tensor, we find the adiabatic and DeWitt-Schwinger expansions of the Green’s function when the space-time points are spatially separated. In two and four dimensions, the resulting DeWitt-Schwinger and adiabatic expansions are identical. In three dimensions, the DeWitt-Schwinger expansion contains terms of adiabatic order 4 that are not necessary for the renormalization of the stress-energy tensor and hence absent in the adiabatic expansion. The equivalence of the DeWitt-Schwinger and adiabatic approaches to renormalization in the scenario considered is thereby demonstrated in even dimensions. In odd dimensions the situation is less clear and further investigation is required in order to determine whether adiabatic renormalization is a locally covariant renormalization prescription.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. (https://creativecommons.org/licenses/by/4.0/) Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - HORIZON 2020 777740 SCIENCE AND TECHNOLOGY FACILITIES COUNCIL ST/T001038/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 22 Feb 2023 12:36 |
Last Modified: | 22 Feb 2023 12:36 |
Status: | Published |
Publisher: | American Physical Society (APS) |
Refereed: | Yes |
Identification Number: | 10.1103/physrevd.107.025004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:196660 |