  We study the renormalizability in theories of a self-interacting Lifshitz
scalar field. We show that although the statement of power-counting is true at
one-loop order, in generic cases where the scalar field is dimensionless, an
infinite number of counter terms are involved in the renormalization procedure.
This problem can be avoided by imposing symmetries, the shift symmetry in the
present paper, which allow only a finite number of counter terms to appear. The
symmetry requirements might have important implications for the construction of
matter field sectors in the Horava-Lifshitz gravity.
