Classical and quantum gravity with fractional operators

Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is made of either fractional derivatives or a covariant fractional d'Alembertian. The classical action for each theory is constructed and the equations of motion are derived. Unitarity and renormalizability of theories with a fractional d'Alembertian are also considered. We argue that unitarity and power-counting renormalizability never coexist, although in some cases one-loop unitary and finiteness are possible. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity.

Automated summary

In this work, a class of perturbative theories of quantum gravity based on fractional operators is proposed, with the construction of classical actions and derivation of equations of motion for each theory. The study shows that unitarity and power-counting renormalizability do not coexist in these theories, although one-loop unitarity and finiteness are possible in some cases. One of the theories is found to be unitary and infrared-finite, serving as a ghost-free model with large-scale modifications of general relativity.