  We construct a perturbative expansion of the scalar sector in the
Myers-Pospelov model, up to second order in the Lorentz violating parameter and
taking into account its higher-order time derivative character. This expansion
allows us to construct an hermitian positive-definite Hamiltonian which
provides a correct basis for quantization. Demanding that the modified normal
frequencies remain real requires the introduction of an upper bound in the
magnitude |k| of the momentum, which is a manifestation of the effective
character of the model. The free scalar propagator, including the corresponding
modified dispersion relations, is also calculated to the given order, thus
providing the starting point to consider radiative corrections when
interactions are introduced.
