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 TMF, 2006, Volume 147, Number 2, Pages 290–302 (Mi tmf1964)

Four-loop verification of an algorithm for summing Feynman diagrams in the $N{=}1$ supersymmetric electrodynamics

A. B. Pimenov, K. V. Stepanyantz

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: By calculating some four-loop diagrams in the $N{=}1$ supersymmetric electrodynamics regularized by higher derivatives, we verify a method for summing Feynman diagrams based on using Schwinger–Dyson equations and Ward identities. In particular, for the diagrams considered, we prove the correctness of an additional identity for Green's functions not reduced to the gauge Ward identity.

Keywords: supersymmetry, Ward identity, higher covariant derivatives

DOI: https://doi.org/10.4213/tmf1964

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English version:
Theoretical and Mathematical Physics, 2006, 147:2, 687–697

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Revised: 01.12.2005

Citation: A. B. Pimenov, K. V. Stepanyantz, “Four-loop verification of an algorithm for summing Feynman diagrams in the $N{=}1$ supersymmetric electrodynamics”, TMF, 147:2 (2006), 290–302; Theoret. and Math. Phys., 147:2 (2006), 687–697

Citation in format AMSBIB
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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. K. V. Stepanyantz, “Summation of diagrams in $N=1$ supersymmetric electrodynamics regularized by higher derivatives”, Theoret. and Math. Phys., 146:3 (2006), 321–334
2. K. V. Stepanyantz, “Contribution of matter fields to the Gell-Mann–Low function for the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 150:3 (2007), 377–392
3. A. B. Pimenov, K. V. Stepanyantz, “Two-loop Gell-Mann–Low function of the $N=1$ supersymmetric Yang–Mills theory regularized by higher covariant derivatives”, Theoret. and Math. Phys., 155:3 (2008), 848–861
4. A. B. Pimenov, K. V. Stepanyantz, “Verifying a new identity for Green's functions of the $N=1$ supersymmetric non-Abelian Yang–Mills theory with matter fields”, Theoret. and Math. Phys., 156:2 (2008), 1199–1208
5. Soloshenko AA, Stepan'yants KV, “Schwinger-Dyson Equations for N=1 Supersymmetric Yang-Mills Theory”, Moscow University Physics Bulletin, 63:3 (2008), 189–192
6. Pimenov, AB, “REGULARIZATION BY HIGHER DERIVATIVES AND QUANTUM CORRECTION FOR N=1 SUPERSYMMETRIC THEORIES”, Russian Physics Journal, 51:5 (2008), 444
7. Stepanyantz, KV, “Toward proving a new identity for Green's functions in N=1 supersymmetric electrodynamics”, Physics of Atomic Nuclei, 72:1 (2009), 105
8. Shevtsova, ES, “Structure of the two-point green function of the gauge field for N=1 supersymmetric Yang-Mills theory regularized by higher covariant derivatives”, Moscow University Physics Bulletin, 64:5 (2009), 485
9. Stepanyantz, KV, “A new relation restricting the Green functions of N=1 supersymmetric electrodynamics”, Moscow University Physics Bulletin, 64:3 (2009), 250
10. Stepanyantz K., “Application of Higher Derivative Regularization To Calculation of Quantum Corrections in N=1 Supersymmetric Theories”, Particle Physics on the Eve of Lhc, 2009, 390–393
11. K. V. Stepanyantz, “Higher covariant derivative regularization for calculations in supersymmetric theories”, Proc. Steklov Inst. Math., 272 (2011), 256–265
12. Stepanyantz K.V., “Derivation of the exact NSVZ beta-function in N=1 SQED, regularized by higher derivatives, by direct summation of Feynman diagrams”, Nuclear Phys B, 852:1 (2011), 71–107
13. Stepanyantz K.V., “Factorization of Integrals Defining the beta-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives”, Internat J Theoret Phys, 51:1 (2012), 276–291
14. Stepanyantz K.V., “The Nsvz Beta-Function and the Schwinger-Dyson Equations For N=1 Sqed With N-F Flavors, Regularized By Higher Derivatives”, J. High Energy Phys., 2014, no. 8, 096
15. Stepanyantz K.V., Nucl. Phys. B, 909 (2016), 316–335
16. Shakhmanov V.Yu. Stepanyantz K.V., “New Form of the Nsvz Relation At the Two-Loop Level”, Phys. Lett. B, 776 (2018), 417–423
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