scholarly journals Modified dispersion relations from the renormalization group of gravity

2007 ◽  
Vol 24 (16) ◽  
pp. 3995-4008 ◽  
Author(s):  
F Girelli ◽  
S Liberati ◽  
R Percacci ◽  
C Rahmede
Keyword(s):  
Renormalization Group ◽  
Dispersion Relations ◽  
Modified Dispersion Relations

QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES

2011 ◽  
Vol 20 (05) ◽  
pp. 745-756 ◽  
Author(s):  
FRANCISCO DIEGO MAZZITELLI
Keyword(s):  
Vector Field ◽  
General Structure ◽  
Scalar Fields ◽  
Field Approximation ◽  
Weak Field ◽  
Dispersion Relations ◽  
Quantum Fields ◽  
Renormalization Procedure ◽  
Modified Dispersion Relations ◽  
Weak Field Approximation

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

scholarly journals DISCRETENESS WITHOUT SYMMETRY BREAKING: A THEOREM

2009 ◽  
Vol 24 (32) ◽  
pp. 2579-2587 ◽  
Author(s):  
LUCA BOMBELLI ◽  
JOE HENSON ◽  
RAFAEL D. SORKIN
Keyword(s):  
Symmetry Breaking ◽  
Lorentz Invariance ◽  
Minkowski Spacetime ◽  
Dispersion Relations ◽  
Poisson Processes ◽  
Discrete Structure ◽  
Preferred Frame ◽  
Modified Dispersion Relations ◽  
Measurable Map

This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to "Lorentz breaking" effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

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