S. G. Gorishnii, A. P. Isaev, “An approach to the calculation of many-loop massless Feynman integrals”, TMF, 62:3 (1985), 345–358; Theoret. and Math. Phys., 62:3 (1985), 232

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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 62, Number 3, Pages 345–358 (Mi tmf4652)

This article is cited in 32 scientific papers (total in 32 papers)

An approach to the calculation of many-loop massless Feynman integrals

S. G. Gorishnii, A. P. Isaev

Full-text PDF (1360 kB) Citations (32)

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Abstract: A generalization of the identity of dimensionless regularization, $\int d^{D}k(k^2)^{-\alpha}=0$, $\alpha\ne D/2$ is proposed. The generalization is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals with one external momentum into classes of equal integrals, and also for calculating some of them. A nontrivial symmetry of the propagator integrals is revealed, on the basis of which a complete system of functional equations for determining two-loop integrals is derived. Possible generalizations of these equations are discussed.

Received: 10.04.1984

English version:
Theoretical and Mathematical Physics, 1985, Volume 62, Issue 3, Pages 232–240
DOI: https://doi.org/10.1007/BF01018263

Bibliographic databases:

Language: Russian

Citation: S. G. Gorishnii, A. P. Isaev, “An approach to the calculation of many-loop massless Feynman integrals”, TMF, 62:3 (1985), 345–358; Theoret. and Math. Phys., 62:3 (1985), 232–240

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\crossref{https://doi.org/10.1007/BF01018263}

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Linking options:

https://www.mathnet.ru/eng/tmf4652

https://www.mathnet.ru/eng/tmf/v62/i3/p345

This publication is cited in the following 32 articles:

Dario Benedetti, Razvan Gurau, Sabine Harribey, “Addendum: Long-range multi-scalar models at three loops (2020 J. Phys. A: Math. Theor. 53 445008)”, J. Phys. A: Math. Theor., 58:12 (2025), 129401
I. V. Anikin, “Vacuum Integration: UV- and IR-Divergencies”, Phys. Part. Nuclei Lett., 21:1 (2024), 11
I. V. Anikin, “The Gorishny–Isaev Vacuum Integrations and UV(IR)-Regime”, Phys. Part. Nuclei, 55:4 (2024), 808
S. E. Derkachov, A. P. Isaev, L. A. Shumilov, “Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles”, J. High Energ. Phys., 2023:6 (2023)
Anatoly V. Kotikov, “Effective Quantum Field Theory Methods for Calculating Feynman Integrals”, Symmetry, 16:1 (2023), 52
I. V. Anikin, “Conformal symmetry and effective potential: II. Evolution”, Eur. Phys. J. A, 59:11 (2023)
I V Anikin, “Conformal symmetry and effective potential: I. Vacuum Vz, x operation for the Green functions”, Progress of Theoretical and Experimental Physics, 2023:10 (2023)
S. E. Derkachev, A. V. Ivanov, “Racah Coefficients for the Group SL(2,ℝ)”, J Math Sci, 275:3 (2023), 289
S. E. Derkachev, A. V. Ivanov, “Koeffitsienty Raka dlya gruppy $\mathrm{SL}(2,\mathbb{R})$”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 99–112
Kotikov V A., “Some Examples of Calculation of Massless and Massive Feynman Integrals”, Particles, 4:3 (2021), 361–380
Alessandro Georgoudis, Vasco Goncalves, Erik Panzer, Raul Pereira, Alexander V. Smirnov, Vladimir A. Smirnov, “Glue-and-cut at five loops”, J. High Energ. Phys., 2021:9 (2021)
Marc P. Bellon, Enrico I. Russo, “Ward–Schwinger–Dyson equations in $\phi ^3_6$ quantum field theory”, Lett Math Phys, 111:2 (2021)
I. V. Anikin, “On Vacuum Integration”, Phys. Part. Nuclei Lett., 18:3 (2021), 290
Anatoly V. Kotikov, “About Calculation of Massless and Massive Feynman Integrals”, Particles, 3:2 (2020), 394
S. È. Derkachev, V. P. Spiridonov, “The $6j$-symbols for the $SL(2,\mathbb C)$ group”, Theoret. and Math. Phys., 198:1 (2019), 29–47
Mikhailov S.V. Volchanskiy N., “Two-Loop Kite Master Integral For a Correlator of Two Composite Vertices”, J. High Energy Phys., 2019, no. 1, 202
Kotikov A.V. Teber S., “Multi-Loop Techniques For Massless Feynman Diagram Calculations”, Phys. Part. Nuclei, 50:1 (2019), 1–41
A. V. Kotikov, S. Teber, “New results for a two-loop massless propagator-type Feynman diagram”, Theoret. and Math. Phys., 194:2 (2018), 284–294
Manashov A.N. Strohmaier M., “Correction Exponents in the Gross-Neveu-Yukawa Model At 1/N-2”, Eur. Phys. J. C, 78:6 (2018), 454
Marko Simonović, Tobias Baldauf, Matias Zaldarriaga, John Joseph Carrasco, Juna A. Kollmeier, “Cosmological perturbation theory using the FFTLog: formalism and connection to QFT loop integrals”, J. Cosmol. Astropart. Phys., 2018:04 (2018), 030

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

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