  We explore the possibility that, in a quantum field theory with Planck scale
cutoff Lambda=Mp, 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 "classicalization" scenario. We then show that, by
imposing the result does not depend on Lambda (in the limit Lambda to Mp), 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=Mp.
