Effective potentials in the Lifshitz scalar field theory

Details Effective potentials in the Lifshitz scalar field theory Effective potentials in the Lifshitz scalar field theory

2011-05-26

arxiv.org/abs/1105.5194v3

Phys.Lett.B703:100-105,2011

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 4 figures

Scientific paper

10.1016/j.physletb.2011.07.057

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.

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