Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges

Markus B. Fröb; Mojtaba Taslimi Tehrani

doi:10.1103/PhysRevD.97.025022

Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges

Markus B. Fröb, Mojtaba Taslimi Tehrani

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory.

Original language	English
Number of pages	24
Journal	Physical Review D
Volume	97
DOIs	https://doi.org/10.1103/PhysRevD.97.025022
Publication status	Published - 30 Jan 2018

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

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Cite this

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title = "Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges",

abstract = "We determine the retarded and advanced Green{\textquoteright}s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green{\textquoteright}s functions in terms of derivatives of scalar and vector Green{\textquoteright}s functions, and show how these relations appear as Ward identities in the free quantum theory.",

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N2 - We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory.

AB - We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory.

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