  We study unitarity and renormalizability in the Lifshitz scalar field theory,
which is characterized by an anisotropic scaling between the space and time
directions. Without the Lorentz symmetry, both the unitarity and the
renormalizability conditions are modified from those in relativistic theories.
We show that for renormalizability, an extended version of the power counting
condition is required in addition to the conventional one. The unitarity bound
for S-matrix elements also gives stronger constraints on interaction terms
because of the reference frame dependence of scattering amplitudes. We prove
that both unitarity and renormalizability require identical conditions as in
the case of conventional relativistic theories.
