N. I. Usyukina, “Calculation of many-loop diagrams of perturbation theory”, TMF, 54:1 (1983), 124–129; Theoret. and Math. Phys., 54:1 (1983), 78

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Teoreticheskaya i Matematicheskaya Fizika, 1983, Volume 54, Number 1, Pages 124–129 (Mi tmf4369)

This article is cited in 40 scientific papers (total in 40 papers)

Calculation of many-loop diagrams of perturbation theory

N. I. Usyukina

Full-text PDF (544 kB) Citations (40)

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Abstract: Some identities are formulated for semi-unique vertices and semi-unique triangles that occur in the diagrams of perturbation theory with massless scalar particles. The use of these identities makes it possible to develop a reduction scheme by means of which the result can be obtained for many-loop diagrams without expansion in infinite series in Gegenbauer polynomials and without the use of the operation of differentiation, which leads to additional kinematic complications. As a result, the calculation of many-loop diagrams of the perturbation theory is significantly simplified.

Received: 29.04.1982

English version:
Theoretical and Mathematical Physics, 1983, Volume 54, Issue 1, Pages 78–81
DOI: https://doi.org/10.1007/BF01017127

Bibliographic databases:

Language: Russian

Citation: N. I. Usyukina, “Calculation of many-loop diagrams of perturbation theory”, TMF, 54:1 (1983), 124–129; Theoret. and Math. Phys., 54:1 (1983), 78–81

Citation in format AMSBIB

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\pages 124--129

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\jour Theoret. and Math. Phys.

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\issue 1

\pages 78--81

\crossref{https://doi.org/10.1007/BF01017127}

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Linking options:

https://www.mathnet.ru/eng/tmf4369

https://www.mathnet.ru/eng/tmf/v54/i1/p124

This publication is cited in the following 40 articles:

Paul-Hermann Balduf, Springer Theses, Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory, 2024, 1
Aleksandr V. Ivanov, “Three-loop renormalization of the quantum action for a four-dimensional scalar model with quartic interaction with the usage of the background field method and a cutoff regularization”, Nuclear Physics B, 1006 (2024), 116647
Anatoly V. Kotikov, “Effective Quantum Field Theory Methods for Calculating Feynman Integrals”, Symmetry, 16:1 (2023), 52
Andrei I. Davydychev, York Schröder, “Recursion-free solution for two-loop vacuum integrals with “collinear” masses”, J. High Energ. Phys., 2022:12 (2022)
Kotikov V A., “Some Examples of Calculation of Massless and Massive Feynman Integrals”, Particles, 4:3 (2021), 361–380
Michelangelo Preti, “The Game of Triangles”, J. Phys.: Conf. Ser., 1525:1 (2020), 012015
Anatoly V. Kotikov, “About Calculation of Massless and Massive Feynman Integrals”, Particles, 3:2 (2020), 394
Kotikov A.V. Teber S., “Multi-Loop Techniques For Massless Feynman Diagram Calculations”, Phys. Part. Nuclei, 50:1 (2019), 1–41
Gonzalez I. Kondrashuk I. Notte-Cuello E.A. Parra-Ferrada I., “Multi-Fold Contour Integrals of Certain Ratios of Euler Gamma Functions From Feynman Diagrams: Orthogonality of Triangles”, Anal. Math. Phys., 8:4 (2018), 589–602
S. Teber, A. V. Kotikov, “The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations”, Theoret. and Math. Phys., 190:3 (2017), 446–457
A. V. Kotikov, S. Teber, “Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene”, Phys. Rev. D, 89:6 (2014)
S. Teber, “Two-loop fermion self-energy and propagator in reducedQED3,2”, Phys. Rev. D, 89:6 (2014)
D. I. Kazakov, “Evaluation of multi-box diagrams in six dimensions”, J. High Energ. Phys., 2014:4 (2014)
I. Gonzalez, I. Kondrashuk, “Box ladders in a noninteger dimension”, Theoret. and Math. Phys., 177:2 (2013), 1515–1539
Pedro Allendes, Bernd A. Kniehl, Igor Kondrashuk, Eduardo A. Notte-Cuello, Marko Rojas-Medar, “Solution to Bethe–Salpeter equation via Mellin–Barnes transform”, Nuclear Physics B, 870:1 (2013), 243
A. V. Kotikov, S. Teber, “Note on an application of the method of uniqueness to reduced quantum electrodynamics”, Phys. Rev. D, 87:8 (2013)
Ivan Gonzalez, Igor Kondrashuk, “Belokurov-Usyukina loop reduction in non-integer dimension”, Phys. Part. Nuclei, 44:2 (2013), 268
Vladimir A. Smirnov, Springer Tracts in Modern Physics, 250, Analytic Tools for Feynman Integrals, 2012, 275
Pedro Allendes, Natanael Guerrero, Igor Kondrashuk, Eduardo A. Notte Cuello, “New four-dimensional integrals by Mellin–Barnes transform”, Journal of Mathematical Physics, 51:5 (2010)
Yu. G. Kondrat'ev, A. M. Chebotarev, “Bernstein theorems and transformations of correlation measures in statistical physics”, Math. Notes, 79:5 (2006), 649–663

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	139
References:	48
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