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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 3, Pages 325–336
DOI: https://doi.org/10.4213/tmf8470 (Mi tmf8470) 		 
This article is cited in 10 scientific papers (total in 10 papers)

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

L. Ts. Adzhemyana, M. V. Kompanietsa, S. V. Novikovb, V. K. Sazonova

a Saint Petersburg State University, St. Petersburg, Russia
b Google Switzerland GmbH, Zürich, Switzerland
Full-text PDF (416 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf8470
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
English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 3, Pages 717–726
DOI: https://doi.org/10.1007/s11232-013-0057-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, TMF, 175:3 (2013), 325–336; Theoret. and Math. Phys., 175:3 (2013), 717–726
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:72
    First page:32
     
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