A momentum-space representation of Green's functions with modified dispersion relations on general backgrounds

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Abstract

We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally to a preferred direction, determined by a unit time-like vector field. By assuming that the integral curves of the vector field are geodesics, we expand the modified Klein-Gordon equation in Fermi normal coordinates. By means of a Fourier transform, we find a series representation in momentum-space of the Green's functions. The coefficients of the series are geometrical terms containing combinations of the Ricci tensor and the vector field, as expected from previous calculations with different methods and for specific backgrounds.
Original languageUndefined/Unknown
JournalPhys.Rev.D
DOIs
Publication statusPublished - 26 Mar 2008

Cite this

@article{54efa8a144904eefba94592163948485,
title = "A momentum-space representation of Green's functions with modified dispersion relations on general backgrounds",
abstract = "We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally to a preferred direction, determined by a unit time-like vector field. By assuming that the integral curves of the vector field are geodesics, we expand the modified Klein-Gordon equation in Fermi normal coordinates. By means of a Fourier transform, we find a series representation in momentum-space of the Green's functions. The coefficients of the series are geometrical terms containing combinations of the Ricci tensor and the vector field, as expected from previous calculations with different methods and for specific backgrounds.",
author = "Massimiliano Rinaldi",
note = "Typos corrected, details and comments added. To appear on Physical Review D",
year = "2008",
month = "3",
day = "26",
doi = "10.1103/PhysRevD.78.024025",
language = "Ind{\'e}fini/inconnu",
journal = "Physical Review D - Particles, Fields, Gravitation and Cosmology",
issn = "1550-7998",
publisher = "American Physical Society",

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T1 - A momentum-space representation of Green's functions with modified dispersion relations on general backgrounds

AU - Rinaldi, Massimiliano

N1 - Typos corrected, details and comments added. To appear on Physical Review D

PY - 2008/3/26

Y1 - 2008/3/26

N2 - We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally to a preferred direction, determined by a unit time-like vector field. By assuming that the integral curves of the vector field are geodesics, we expand the modified Klein-Gordon equation in Fermi normal coordinates. By means of a Fourier transform, we find a series representation in momentum-space of the Green's functions. The coefficients of the series are geometrical terms containing combinations of the Ricci tensor and the vector field, as expected from previous calculations with different methods and for specific backgrounds.

AB - We consider the problem of calculating the Green's functions associated to a massive scalar field with modified dispersion relations. We analyze the case when dispersion is modified by higher derivative spatial operators acting on the field orthogonally to a preferred direction, determined by a unit time-like vector field. By assuming that the integral curves of the vector field are geodesics, we expand the modified Klein-Gordon equation in Fermi normal coordinates. By means of a Fourier transform, we find a series representation in momentum-space of the Green's functions. The coefficients of the series are geometrical terms containing combinations of the Ricci tensor and the vector field, as expected from previous calculations with different methods and for specific backgrounds.

U2 - 10.1103/PhysRevD.78.024025

DO - 10.1103/PhysRevD.78.024025

M3 - Article

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

ER -