Geodesic
Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals: Proof of the~main relation
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 325-336

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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. 
@article{TMF_2013_175_3_a0,
     author = {L. Ts. Adzhemyan and M. V. Kompaniets and S. V. Novikov and V. K. Sazonov},
     title = {Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals: {Proof} of the~main relation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {325--336},
     publisher = {mathdoc},
     volume = {175},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a0/}
}
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L. Ts. Adzhemyan; M. V. Kompaniets; S. V. Novikov; V. K. Sazonov. Representation of the~$\beta$-function and anomalous dimensions by nonsingular integrals: Proof of the~main relation. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 325-336. http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a0/