Momentum-space representation of Green’s functions with modified dispersion relations on general backgrounds

Massimiliano Rinaldi
Phys. Rev. D 78, 024025 – Published 11 July 2008

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 timelike 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.

  • Figure
  • Received 30 April 2008

DOI:https://doi.org/10.1103/PhysRevD.78.024025

©2008 American Physical Society

Authors & Affiliations

Massimiliano Rinaldi

  • Département de Physique Théorique, Université de Genève, 24, quai E. Ansermet 1211 Genève 4, Switzerland

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Issue

Vol. 78, Iss. 2 — 15 July 2008

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