Standard

Renormalization group and the e{open}-expansion : Representation of the β-function and anomalous dimensions by nonsingular integrals. / Adzhemyan, L. Ts; Kompaniets, M. V.

In: Theoretical and Mathematical Physics, Vol. 169, No. 1, 01.10.2011, p. 1450-1459.

Research output: Contribution to journal › Article › peer-review

Harvard

Adzhemyan, LT & Kompaniets, MV 2011, 'Renormalization group and the e{open}-expansion: Representation of the β-function and anomalous dimensions by nonsingular integrals', Theoretical and Mathematical Physics, vol. 169, no. 1, pp. 1450-1459. https://doi.org/10.1007/s11232-011-0121-z

APA

Adzhemyan, L. T., & Kompaniets, M. V. (2011). Renormalization group and the e{open}-expansion: Representation of the β-function and anomalous dimensions by nonsingular integrals. Theoretical and Mathematical Physics, 169(1), 1450-1459. https://doi.org/10.1007/s11232-011-0121-z

Vancouver

Adzhemyan LT, Kompaniets MV. Renormalization group and the e{open}-expansion: Representation of the β-function and anomalous dimensions by nonsingular integrals. Theoretical and Mathematical Physics. 2011 Oct 1;169(1):1450-1459. https://doi.org/10.1007/s11232-011-0121-z

Author

Adzhemyan, L. Ts ; Kompaniets, M. V. / Renormalization group and the e{open}-expansion : Representation of the β-function and anomalous dimensions by nonsingular integrals. In: Theoretical and Mathematical Physics. 2011 ; Vol. 169, No. 1. pp. 1450-1459.

BibTeX

@article{6760d584a2f3486e863793bdc1e86fe3,
title = "Renormalization group and the e{open}-expansion: Representation of the β-function and anomalous dimensions by nonsingular integrals",
abstract = "In the framework of the renormalization group and the e{open}-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in e{open}. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ3 model in the order e{open}4.",
keywords = "critical exponents, e{open}-expansion, multiloop diagrams, renormalization group",
author = "Adzhemyan, {L. Ts} and Kompaniets, {M. V.}",
year = "2011",
month = oct,
day = "1",
doi = "10.1007/s11232-011-0121-z",
language = "English",
volume = "169",
pages = "1450--1459",
journal = "Theoretical and Mathematical Physics (Russian Federation)",
issn = "0040-5779",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Renormalization group and the e{open}-expansion

T2 - Representation of the β-function and anomalous dimensions by nonsingular integrals

AU - Adzhemyan, L. Ts

AU - Kompaniets, M. V.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - In the framework of the renormalization group and the e{open}-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in e{open}. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ3 model in the order e{open}4.

AB - In the framework of the renormalization group and the e{open}-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in e{open}. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ3 model in the order e{open}4.

KW - critical exponents

KW - e{open}-expansion

KW - multiloop diagrams

KW - renormalization group

UR - http://www.scopus.com/inward/record.url?scp=80655131249&partnerID=8YFLogxK

U2 - 10.1007/s11232-011-0121-z

DO - 10.1007/s11232-011-0121-z

M3 - Article

VL - 169

SP - 1450

EP - 1459

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -

ID: 36313120