Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?

Abstract

We discuss the applicability of the argument of Collins, Pérez, Sudarsky, Urrutia and Vucetich to loop quantum gravity. This argument suggests that Lorentz violations, even ones that only manifest themselves at energies close to the Planck scale, have significant observational consequences at low energies when one considers perturbative quantum field theory and renormalization. We show that non-perturbative treatments like those of loop quantum gravity may generate deviations of Lorentz invariance of a different type than those considered by Collins et al. that do not necessarily imply observational consequences at low energy.

Figures (1)

• Figure 1: Feynman diagram for the lowest order self-energy. The diagram includes an unbound integral in $k$ that can, for energy dependent Lorentz violations, lead to large observable effects even if the Lorentz violations are small for low energies.