This article is cited in 10 papers

Representation of the $\beta$-function and anomalous dimensions by nonsingular integrals: Proof of the main relation

L. Ts. Adzhemyan^a, M. V. Kompaniets^a, S. V. Novikov^b, V. K. Sazonov<sup>a

a</sup> Saint Petersburg State University, St. Petersburg, Russia
^b Google Switzerland GmbH, Zürich, Switzerland

Abstract: A method for calculating the $\beta$-function and anomalous dimensions, convenient for numerical calculations in the $\varepsilon$-expansion framework, was previously proposed, and the relation underlying the method was verified up to the four-loop approximation. We prove this relation in all orders of the perturbation theory.

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

Received: 19.12.2012

DOI: 10.4213/tmf8470

 English version: Theoretical and Mathematical Physics, 2013, 175:3, 717–726

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