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Teoreticheskaya i Matematicheskaya Fizika, 1983, Volume 56, Number 3, Pages 350–356 (Mi tmf2218)  

This article is cited in 19 scientific papers (total in 19 papers)

An algorithm for calculating multiloop integrals

F. V. Tkachev
References:
Abstract: A class of p integrals which arise in perturbative calculations of some problems in quantum field theory is considered. An algorithm of analytic calculation of any p integral at the three-loop level convenient for realization in the existing systems of analytic calculation is constructed.
Received: 17.05.1982
English version:
Theoretical and Mathematical Physics, 1983, Volume 56, Issue 3, Pages 866–870
DOI: https://doi.org/10.1007/BF01086253
Bibliographic databases:
Language: Russian
Citation: F. V. Tkachev, “An algorithm for calculating multiloop integrals”, TMF, 56:3 (1983), 350–356; Theoret. and Math. Phys., 56:3 (1983), 866–870
Citation in format AMSBIB
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\by F.~V.~Tkachev
\paper An algorithm for calculating multiloop integrals
\jour TMF
\yr 1983
\vol 56
\issue 3
\pages 350--356
\mathnet{http://mi.mathnet.ru/tmf2218}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=721307}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 56
\issue 3
\pages 866--870
\crossref{https://doi.org/10.1007/BF01086253}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1983SL29700003}
Linking options:
  • https://www.mathnet.ru/eng/tmf2218
  • https://www.mathnet.ru/eng/tmf/v56/i3/p350
  • This publication is cited in the following 19 articles:
    1. Xin Guan, Xiang Li, Yan-Qing Ma, “Exploring the linear space of Feynman integrals via generating functions”, Phys. Rev. D, 108:3 (2023)  crossref
    2. J. Blümlein, P. Marquard, C. Schneider, K. Schönwald, “The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements”, J. High Energ. Phys., 2022:1 (2022)  crossref
    3. Andrei I. Davydychev, York Schröder, “Recursion-free solution for two-loop vacuum integrals with “collinear” masses”, J. High Energ. Phys., 2022:12 (2022)  crossref
    4. J. Blümlein, P. Marquard, C. Schneider, K. Schönwald, “The massless three-loop Wilson coefficients for the deep-inelastic structure functions F2, FL, xF3 and g1”, J. High Energ. Phys., 2022:11 (2022)  crossref
    5. B. Ruijl, T. Ueda, J.A.M. Vermaseren, “Forcer, a Form program for the parametric reduction of four-loop massless propagator diagrams”, Computer Physics Communications, 253 (2020), 107198  crossref
    6. Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032  crossref  mathscinet  zmath  isi  scopus
    7. T Ueda, B Ruijl, J A M Vermaseren, “Efficient reduction of four-loop massless propagators”, J. Phys.: Conf. Ser., 920 (2017), 012002  crossref
    8. Michael I. Buchoff, Michael Wagman, “Perturbative renormalization of neutron-antineutron operators”, Phys. Rev. D, 93:1 (2016)  crossref
    9. T Ueda, B Ruijl, J A M Vermaseren, “Calculating four-loop massless propagators with Forcer”, J. Phys.: Conf. Ser., 762 (2016), 012060  crossref
    10. B. Ruijl, T. Ueda, J.A.M. Vermaseren, “The diamond rule for multi-loop Feynman diagrams”, Physics Letters B, 746 (2015), 347  crossref
    11. A. Mitov, S. Moch, “QCD corrections to semi-inclusive hadron production in electron–positron annihilation at two loops”, Nuclear Physics B, 751:1-2 (2006), 18  crossref
    12. J.A.M. Vermaseren, A. Vogt, S. Moch, “The third-order QCD corrections to deep-inelastic scattering by photon exchange”, Nuclear Physics B, 724:1-2 (2005), 3  crossref
    13. Ferroglia, A, “Two-loop vertices in quantum field theory: infrared convergent scalar configurations”, Nuclear Physics B, 680:1–3 (2004), 199  crossref  isi
    14. S. Moch, J.A.M. Vermaseren, A. Vogt, “The QCD Splitting Functions at Three Loops: Methods and Results”, Nuclear Physics B - Proceedings Supplements, 135 (2004), 137  crossref
    15. J.A.M Vermaseren, S Moch, A Vogt, “First results for three-loop deep-inelastic structure functions in QCD”, Nuclear Physics B - Proceedings Supplements, 116 (2003), 100  crossref
    16. S. Moch, J.A.M. Vermaseren, A. Vogt, “Non-singlet structure functions at three loops: Fermionic contributions”, Nuclear Physics B, 646:1-2 (2002), 181  crossref
    17. Passarino, G, “An approach toward the numerical evaluation of multi-loop Feynman diagrams”, Nuclear Physics B, 619:1–3 (2001), 257  crossref  isi
    18. E. E. Boos, A. I. Davydychev, “A method of calculating massive Feynman integrals”, Theoret. and Math. Phys., 89:1 (1991), 1052–1064  mathnet  crossref  mathscinet  isi
    19. L. R. Surguladze, F. V. Tkachev, “Coefficient functions of gluon and quark condensates in QCD sum rules for light vector mesons in the two-loop approximation”, Theoret. and Math. Phys., 75:2 (1988), 502–509  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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