By means of simple models in a flat spacetime manifold we examine some of the issues that arise when quantizing interacting quantum fields in multimetric backgrounds. In particular we investigate the maintenance of a causal structure in the models. In this context we introduce and explain the relevance of an interpolating metric that is a superposition of the individual metrics in the models. We study the renormalization of a model with quartic interactions and elucidate the structure of the renormalization group and its implications for Lorentz symmetry breakdown.

• Received 20 May 2013

DOI:https://doi.org/10.1103/PhysRevD.88.025009