Lorentz invariance without trans-Planckian physics?

We explore the possibility that, in a quantum field theory with Planck scale cutoff Lambda similar or equal to m(p), observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Pi to the self-energy of a scalar field with lambda phi(4) interaction, using a modified (non-invariant) propagator which vanishes in the trans-Planckian regime, as expected in the "classicalisation" scenario. We then show that, by imposing the result does not depend on Lambda (in the limit Lambda -> m(p)), an explicit (albeit not unique) expression for Pi can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff Lambda = m(p). (C) 2013 Elsevier B.V. All rights reserved.