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Teoreticheskaya i Matematicheskaya Fizika, 1974, Volume 18, Number 3, Pages 299–309 (Mi tmf3544)  

This article is cited in 19 scientific papers (total in 19 papers)

Proof of the 3-irreducibility of the third Legendre transform

Yu. M. Pis'mak
References:
Abstract: The iterative solution of the equations of motion [6] for the third Legendre transform is analyzed and it is shown that the graphs obtained in the process of iterating these equations are 3-irreducible. Knowledge of the symmetry coefficients of the graphs is not required for the proof.
Received: 15.02.1973
English version:
Theoretical and Mathematical Physics, 1974, Volume 18, Issue 3, Pages 211–218
DOI: https://doi.org/10.1007/BF01035640
Bibliographic databases:
Language: Russian
Citation: Yu. M. Pis'mak, “Proof of the 3-irreducibility of the third Legendre transform”, TMF, 18:3 (1974), 299–309; Theoret. and Math. Phys., 18:3 (1974), 211–218
Citation in format AMSBIB
\Bibitem{Pis74}
\by Yu.~M.~Pis'mak
\paper Proof of the 3-irreducibility of the third Legendre transform
\jour TMF
\yr 1974
\vol 18
\issue 3
\pages 299--309
\mathnet{http://mi.mathnet.ru/tmf3544}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=468705}
\transl
\jour Theoret. and Math. Phys.
\yr 1974
\vol 18
\issue 3
\pages 211--218
\crossref{https://doi.org/10.1007/BF01035640}
Linking options:
  • https://www.mathnet.ru/eng/tmf3544
  • https://www.mathnet.ru/eng/tmf/v18/i3/p299
  • This publication is cited in the following 19 articles:
    1. A. L. Pismenskii, Yu. M. Pis'mak, “Scaling violation and the appearance of mass in scalar quantum field theories”, Theoret. and Math. Phys., 217:1 (2023), 1495–1504  mathnet  crossref  crossref  mathscinet  adsnasa
    2. Kilian Fraboulet, Jean-Paul Ebran, “Addressing energy density functionals in the language of path-integrals I: comparative study of diagrammatic techniques applied to the (0 + 0)-D O(N)-symmetric φ4-theory”, Eur. Phys. J. A, 59:4 (2023)  crossref
    3. Christian J. Eckhardt, Patrick Kappl, Anna Kauch, Karsten Held, “A functional-analysis derivation of the parquet equation”, SciPost Phys., 15:5 (2023)  crossref
    4. Bagaev A.A. Pis'mak Yu.M., “The 0D Quantum Field Theory: Multiple Integrals Via Background Field Formalism”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), ed. Motygin O. Kiselev A. Kapitanova P. Goray L. Kazakov A. Kirpichnikova A., IEEE, 2016, 41–45  isi
    5. Aleksei A. Bagaev, Yuri M. Pis'mak, 2016 Days on Diffraction (DD), 2016, 41  crossref
    6. Bagaev A.A., “Effektivnoe deistvie v formalizme fonovogo polya”, Vestnik sankt-peterburgskogo universiteta. seriya 4: fizika. khimiya, 2012, no. 3, 56–65 An effective action in the background field formalism /  elib
    7. Christian Brouder, Quantum Field Theory, 2009, 163  crossref
    8. S. Yokojima, M. Komachiya, R. Fukuda, “Derivation of Bethe-Salpeter type N-body bound state equation”, Nuclear Physics B, 390:2 (1993), 319  crossref
    9. M. Komachiya, R. Fukuda, “On-shell expansion of effective action and quark-line diagrams in quantum chromodynamics”, Phys. Rev. D, 46:6 (1992), 2602  crossref
    10. Alan Cooper, Joel Feldman, Lon Rosen, “Cluster irreducibility of the third and fourth Legendre transforms in quantum field theory”, Phys. Rev. D, 25:6 (1982), 1565  crossref
    11. Alan Cooper, Joel Feldman, Lon Rosen, “Higher Legendre transforms and their relationship to Bethe–Salpeter kernels and r-field projectors”, Journal of Mathematical Physics, 23:5 (1982), 846  crossref
    12. V. E. Rochev, “Legendre transformations and equations for Green's functions”, Theoret. and Math. Phys., 47:2 (1981), 397–405  mathnet  crossref  mathscinet  isi
    13. Alan Cooper, Joel Feldman, Lon Rosen, “Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework”, Annals of Physics, 137:2 (1981), 213  crossref
    14. Edward B. Manoukian, “Vacuum Energy‐Density in Quantum Electrodynamics”, Fortschr. Phys., 24:6 (1976), 325  crossref
    15. Yu. M. Pis'mak, “Combinatorial analysis of the overlapping problem for vertices with more than four legs”, Theoret. and Math. Phys., 24:1 (1975), 649–658  mathnet  crossref  mathscinet  zmath
    16. Yu. M. Pis'mak, “Combinational analysis of the overlapping problem for vertices with more than four legs. II. Higher Legendre transforms”, Theoret. and Math. Phys., 24:2 (1975), 755–767  mathnet  crossref  mathscinet  zmath
    17. A. N. Vasil'ev, A. K. Kazanskii, Yu. M. Pis'mak, “Equations for higher Legendre transforms in terms of 1-irreducible vertices”, Theoret. and Math. Phys., 19:2 (1974), 443–453  mathnet  crossref
    18. A. N. Vasil'ev, A. K. Kazanskii, Yu. M. Pis'mak, “Diagrammatic analysis of the fourth Legendre transform”, Theoret. and Math. Phys., 20:2 (1974), 754–762  mathnet  crossref
    19. A. K. Kazanskii, “Equations for Green's functions obtained from a variational principle”, Theoret. and Math. Phys., 21:1 (1974), 927–934  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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