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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1052–1074 (Mi izv2505)  

This article is cited in 10 scientific papers (total in 10 papers)

On summation of the contributions from the Feynman diagrams. An existence theorem

D. Ya. Petrina


Abstract: A method is proposed for the summation of the series of contributions from Feynman diagrams. The proof is given of an existence theorem for the solution of an equation which arises in the summation of series of contributions.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1005–1025

Bibliographic databases:

UDC: 517.9
MSC: 81T18, 34B27, 34A12, 47B25, 40A05, 45A05
Received: 04.07.1967

Citation: D. Ya. Petrina, “On summation of the contributions from the Feynman diagrams. An existence theorem”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1052–1074; Math. USSR-Izv., 2:5 (1968), 1005–1025

Citation in format AMSBIB
\Bibitem{Pet68}
\by D.~Ya.~Petrina
\paper On summation of the contributions from the Feynman diagrams. An
existence theorem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1052--1074
\mathnet{http://mi.mathnet.ru/izv2505}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=266538}
\zmath{https://zbmath.org/?q=an:0175.53101|0186.58203}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1005--1025
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000691}


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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. Ya. Petrina, “Hamiltonians of quantum statistics and the model Hamiltonian of the theory of superconductivity”, Theoret. and Math. Phys., 4:2 (1970), 916–928  mathnet  crossref  mathscinet  zmath
    2. S. S. Ivanov, A. L. Rebenko, “Convergence of perturbation series in field theory models containing fermions”, Theoret. and Math. Phys., 11:2 (1972), 440–450  mathnet  crossref  mathscinet
    3. A. L. Rebenko, “On equations for the matrix elements of Euclidean quantum electrodynamics”, Theoret. and Math. Phys., 11:3 (1972), 525–536  mathnet  crossref  mathscinet
    4. S. S. Ivanov, D. Ya. Petrina, A. L. Rebenko, “On equations for the coefficient functions of the $S$-matrix in quantum field theory”, Theoret. and Math. Phys., 19:1 (1974), 332–339  mathnet  crossref
    5. E. B. Gledzer, A. S. Monin, “The method of diagrams in perturbation theory”, Russian Math. Surveys, 29:3 (1974), 117–168  mathnet  crossref  mathscinet  zmath
    6. S. S. Ivanov, D. Ya. Petrina, A. L. Rebenko, “$S$ matrix in constructive quantum field theory”, Theoret. and Math. Phys., 23:2 (1975), 422–434  mathnet  crossref  mathscinet
    7. V. A. Golubeva, “Some problems in the analytic theory of Feynman integrals”, Russian Math. Surveys, 31:2 (1976), 139–207  mathnet  crossref  zmath
    8. V. I. Skripnik, “Structure of translation operators in the phase spaces of free Euclidean fields. I”, Theoret. and Math. Phys., 35:1 (1978), 292–294  mathnet  crossref  mathscinet  zmath
    9. I. D. Chueshov, “Probability structure of a class of equations for the $S$-matrix in boson theory”, Theoret. and Math. Phys., 37:1 (1978), 855–862  mathnet  crossref  mathscinet
    10. Van Sifu, Xue Kang, “Investigation of equations for coefficient functions of the Yang–Mills field and their solutions”, Theoret. and Math. Phys., 73:1 (1987), 1040–1049  mathnet  crossref  mathscinet  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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