Field Theory at a Lifshitz Point

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.