This article is cited in 1 paper

Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals in models of critical dynamics

L. Ts. Adzhemyan, S. E. Vorobyeva, M. V. Kompaniets

St. Petersburg State University, St. Petersburg, Russia

Abstract: We propose a method for calculating the $\beta$-function and anomalous dimensions in critical dynamics models that is convenient for numerical calculations in the framework of the renormalization group and $\varepsilon$-expansion. Those quantities are expressed in terms of the renormalized Green's function, which is renormalized using the operation $R$ represented in a form that allows reducing ultraviolet divergences of Feynman diagrams explicitly. The integrals needed for the calculation do not contain poles in $\varepsilon$ and are convenient for numerical integration.

Keywords: renormalization group, $\varepsilon$-expansion, multiloop diagram, critical exponent.

DOI: 10.4213/tmf8911

 English version: Theoretical and Mathematical Physics, 2015, 185:1, 1361–1369

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