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TMF, 1980, Volume 44, Number 3, Pages 307–320 (Mi tmf3619)  

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

Infrared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. I

V. A. Smirnov


Abstract: Conditions of the presence of infrared and ultraviolet divergences of coefficient functions corresponding to arbitrary scalar Feynman diagrams and considered as tempered distributions are found. Analytical regularisation is used to analyse both types of divergences. It is shown that for any graph $\Gamma$ there is a domain of regularising complex parameters $\lambda_l$ in which the corresponding coefficient function is an analytical function of these parameters (in the distribution theory sense) possessing analytical continuation into all of $C^{\mathscr L}$ as a meromorphic function with two series of poles (“ultraviolet” and “infrared” ones). Infrared poles are located on hyperplanes defined by relationships: $\sum_{l\in\gamma}\lambda_l=-\Omega^\Gamma(\gamma)+n$, $n=0,1,…$ and $\Omega^\Gamma(\gamma)$ being the index of infrared divergency of a subgraph $\gamma$ of the graph $\Gamma$. These relationships are to be written for the graphs including massless particles only.

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English version:
Theoretical and Mathematical Physics, 1980, 44:3, 761–770

Bibliographic databases:

Received: 03.08.1979

Citation: V. A. Smirnov, “Infrared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. I”, TMF, 44:3 (1980), 307–320; Theoret. and Math. Phys., 44:3 (1980), 761–770

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\jour Theoret. and Math. Phys.
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    This publication is cited in the following articles:
    1. V. A. Smirnov, “Singularities of feynman amplitudes in the momentum space”, Theoret. and Math. Phys., 47:1 (1981), 369–371  mathnet  crossref  mathscinet  isi
    2. V. A. Smirnov, “The singularities of Feynman diagrams in the coordinate space and the $\alpha$-representation”, Theoret. and Math. Phys., 46:1 (1981), 17–21  mathnet  crossref  mathscinet  isi
    3. V. A. Smirnov, “In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. II”, Theoret. and Math. Phys., 46:2 (1981), 132–140  mathnet  crossref  mathscinet  isi
    4. S. A. Anikin, V. A. Smirnov, “Analytic renormalization of massless theories”, Theoret. and Math. Phys., 51:1 (1982), 317–321  mathnet  crossref  mathscinet  isi
    5. V. A. Smirnov, K. G. Chetyrkin, “Dimensional regularization and infrared divergences”, Theoret. and Math. Phys., 56:2 (1983), 770–776  mathnet  crossref  mathscinet  isi
    6. V. A. Smirnov, “Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes”, Theoret. and Math. Phys., 59:3 (1984), 563–573  mathnet  crossref  mathscinet  isi
    7. S. A. Anikin, V. A. Smirnov, “The R operation in theories with massless particles”, Theoret. and Math. Phys., 60:1 (1984), 664–670  mathnet  crossref  mathscinet  isi
    8. D. I. Kazakov, “Many-loop calculations: The uniqueness method and functional equations”, Theoret. and Math. Phys., 62:1 (1985), 84–89  mathnet  crossref  isi
    9. V. A. Smirnov, K. G. Chetyrkin, “$R^*$ operation in the minimal subtraction scheme”, Theoret. and Math. Phys., 63:2 (1985), 462–469  mathnet  crossref  mathscinet  isi
    10. A. I. Zaslavskii, “Behavior of massless feynman integrals near singular points”, Theoret. and Math. Phys., 80:3 (1989), 935–941  mathnet  crossref  mathscinet  isi
    11. É. Yu. Lerner, “Feynman integrals of $p$-adic argument in momentum space III. Renormalization”, Theoret. and Math. Phys., 106:2 (1996), 195–208  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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