Abstract
We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type. For these specific form factors, which appear in some renormalizable theories, the number of field degrees of freedom and of initial conditions is finite.
Highlights
We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type
Nonlocal quantum gravity has achieved a high degree of independence both from these antecedents and from other proposals, to the point where it can be considered as one of the most promising and accessible candidates for a theory where the gravitational force consistently obeys the laws of quantum mechanics
The Lagrangian Lφ is second-order in spacetime derivatives and features one local field φ, there is only 1 degrees of freedom (DOF) and solutions are specified by two initial conditions
Summary
“Nonlocal quantum gravity” is an umbrella name including at least two different settings. Examples are the approaches by Woodard and Maggiore (and collaborators) [1,2,3,4,5] In this brief review of recent results, we will confine ourselves to the second meaning of the term, where nonlocality is fundamentally present already at the classical level and, thanks to the suppression of the graviton propagator in the ultraviolet (UV), the theory is renormalizable or finite. Mainly developed with discontinuous effort from the 1970s to the 1990s by Alebastrov, Efimov, Krasnikov, Kuz’min, Moffat and Tomboulis among others [6,7,8,9,10,11], nonlocal operators were early recognized as an opportunity to improve the renormalization properties of scalar [6,7,8] and gauge [9,10,12] field theories, with some interest in gravity [10,11].
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