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.

Nonlocal Gravity

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
Gravitational Field ◽  
Gravitational Lensing ◽  
Past History ◽  
Lorentz Invariance ◽  
Minkowski Spacetime ◽  
Field Measurements ◽  
Local Principle ◽  
History Of ◽  
Expansion Of The Universe ◽  
Nearby Galaxies

A postulate of locality permeates through the special and general theories of relativity. First, Lorentz invariance is extended in a pointwise manner to actual, namely, accelerated observers in Minkowski spacetime. This hypothesis of locality is then employed crucially in Einstein’s local principle of equivalence to render observers pointwise inertial in a gravitational field. Field measurements are intrinsically nonlocal, however. To go beyond the locality postulate in Minkowski spacetime, the past history of the accelerated observer must be taken into account in accordance with the Bohr-Rosenfeld principle. The observer in general carries the memory of its past acceleration. The deep connection between inertia and gravitation suggests that gravity could be nonlocal as well and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein’s theory of gravitation has recently been developed. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. A significant observational consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. The implications of NLG are explored in this book for gravitational lensing, gravitational radiation, the gravitational physics of the Solar System and the internal dynamics of nearby galaxies as well as clusters of galaxies. This approach is extended to nonlocal Newtonian cosmology, where the attraction of gravity fades with the expansion of the universe. Thus far only some of the consequences of NLG have been compared with observation.

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 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
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