Effective potentials in the Lifshitz scalar field theory

TL;DR

This paper analyzes the one-loop effective potentials of a four-dimensional Lifshitz scalar field theory with anisotropic scaling z=2, demonstrating improved UV behavior, IR divergence resolution, and implications for symmetry breaking and phase transitions.

Contribution

It shows renormalization without coupling constant renormalization and addresses IR divergences in the Lifshitz scalar field theory, providing new insights into its quantum behavior.

Findings

Renormalization is achievable without coupling constant renormalization.

IR divergences are resolved in the massless case.

Conditions for symmetry breaking and critical temperature existence are derived.

Abstract

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. The physical consequences of the other logarithmic divergence free model is discussed.