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 TMF, 1985, Volume 62, Number 1, Pages 127–135 (Mi tmf4536)

This article is cited in 11 scientific papers (total in 11 papers)

Many-loop calculations: The uniqueness method and functional equations

D. I. Kazakov

Abstract: In the framework of the calculation of many-loop Feynman integrals – the uniqueness method – functional equations are obtained for the coefficient functions of the diagrams. Solution of a functional equation leads to calculation of an $N$-shaped diagram, the last of the 5-loop diagrams of the $\varphi^4$ theory. The obtained result makes it possible to extend by an order the tables constructed previously for the calculation of many-loop integrals.

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English version:
Theoretical and Mathematical Physics, 1985, 62:1, 84–89

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Received: 16.01.1984

Citation: D. I. Kazakov, “Many-loop calculations: The uniqueness method and functional equations”, TMF, 62:1 (1985), 127–135; Theoret. and Math. Phys., 62:1 (1985), 84–89

Citation in format AMSBIB
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\by D.~I.~Kazakov
\paper Many-loop calculations: The uniqueness method and functional equations
\jour TMF
\yr 1985
\vol 62
\issue 1
\pages 127--135
\mathnet{http://mi.mathnet.ru/tmf4536}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 62
\issue 1
\pages 84--89
\crossref{https://doi.org/10.1007/BF01034829}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985ANK4300010}

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

This publication is cited in the following articles:
1. D. I. Kazakov, A. V. Kotikov, “Uniqueness method: Multiloop calculations in QCD”, Theoret. and Math. Phys., 73:3 (1987), 1264–1274
2. A. V. Kotikov, “Method of calculating the moments of the structure functions of deep inelastic scattering in quantum chromodynamics”, Theoret. and Math. Phys., 78:2 (1989), 134–143
3. A. L. Pismenskii, “Calculation of the critical index $\eta$ for the $\varphi^3$ theory by the conformal bootstrap method”, Theoret. and Math. Phys., 185:1 (2015), 1516–1521
4. Pismensky A.L., “Calculation of Critical Index Eta of the Phi(3)-Theory in Four-Loop Approximation By the Conformal Bootstrap Technique”, Int. J. Mod. Phys. A, 30:24 (2015), 1550138
5. Pismensky A.L., Pis'mak Yu.M., “Scaling Violation in Massless Scalar Quantum Field Models in Logarithmic Dimensions”, J. Phys. A-Math. Theor., 48:32, SI (2015), 325401
6. 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
7. 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
8. Gracey J.A., “Large N-F Quantum Field Theory”, Int. J. Mod. Phys. A, 33:35 (2018), 1830032
9. Pismensky A.L., “Application of Eta-Expansion Technique to the Phi(3)-Theory in Arbitrary Dimension”, Int. J. Mod. Phys. A, 33:35 (2018), 1850209
10. 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
11. Kotikov A.V. Teber S., “Multi-Loop Techniques For Massless Feynman Diagram Calculations”, Phys. Part. Nuclei, 50:1 (2019), 1–41
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