Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-02-08
Physics
High Energy Physics
High Energy Physics - Theory
10 pages
Scientific paper
In this paper we consider the relation between the super-renormalizable theories of quantum gravity (SRQG) studied in [arXiv:1110.5249v2, arXiv:1202.0008] and an underlying non-commutativity of spacetime. For one particular super-renormalizable theory we show that at linear level (quadratic in the Lagrangian) the propagator of the theory is the same we obtain starting from a theory of gravity endowed with {\theta}-Poincar\'e quantum groups of symmetry. Such a theory is over the so called {\theta}-Minkowski non-commuative spacetime. We shed new light on this link and show that among the theories considered in [arXiv:1110.5249v2, arXiv:1202.0008], there exist only one non-local and Lorentz invariant super-renormalizable theory of quantum gravity that can be described in terms of a quantum group symmetry structure. We also emphasize contact with pre-existent works in the literature and discuss preservation of the equivalence principle in our framework.
Alexander Stephon
Marciano Antonino
Modesto Leonardo
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