Renormalization in theories with modified dispersion relations: weak gravitational fields

Details Renormalization in theories with modified dispersion relations: weak gravitational fields Renormalization in theories with modified dispersion relations: weak gravitational fields

2008-10-16

arxiv.org/abs/0810.2922v1

Phys.Lett.B672:294-298,2009

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, no figures

Scientific paper

10.1016/j.physletb.2009.01.025

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein-Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of <\phi^2> and , working in the weak field approximation. We show that for dispersion relations containing up to $2s$ powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on $s$ in a qualitatively different way: while <\phi^2> becomes convergent for a sufficiently large value of $s$, the number of divergent terms in the adiabatic expansion of increases with $s$. This property was not apparent in previous results for spatially homogeneous backgrounds.

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