  We construct the general renormalizable actions for the scalar field and the
gauge field at a Lifshitz point characterized by the dynamical critical
exponent $z$. The Lorentz invariance is broken down in the UV region, but is
recovered in the IR limit. Even though the theories are UV complete, the speed
of light is related to the momentum by $z(k/M)^{z-1}$ which can go to infinity
in the UV limit for $z\geq 2$. Since the Lorentz invariance is broken down, the
dispersion relation is modified and the time delays in Gamma-Ray bursts can be
easily explained. In addition, we also discuss the thermal dynamics and the
size of causal patch in a FRW universe for the field theory at a Lifshitz
point.
