Effective potentials in the Lifshitz scalar field theory

Understand

We study the one-loop effective potentials of the four-dimensional Lifshitz scalar field theory with the particular anisotropic scaling $z=2$, and show that the renormalization is possible without resort to the renormalization of the coupling constant due to the improvement of UV divergence.

• Moreover, the IR divergence can be also solved for the massless case of $m^2 =0$, because of the absence of the logarithmic divergence.
• For a massive case, we obtain a condition for the symmetry breaking.
• Finally, we investigate whether the critical temperature can exist or not in this approximation.