  We study the Infra Red (IR) limit of dispersion relations for scalar and
fermion fields in a Lifshitz-type Yukawa model, after dressing by quantum
fluctuations. Relativistic-like dispersion relations emerge dynamically in the
IR regime of the model, after quantum corrections are taken into account. In
this regime, dynamical mass generation also takes place, but in such a way that
the particle excitations remain massive, even if the bare masses vanish. The
group velocities of the corresponding massive particles of course are smaller
than the speed of light, in a way consistent with the IR regime where the
analysis is performed. We also comment on possible extensions of the model
where the fermions are coupled to an Abelian gauge field.
