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 TMF, 1974, Volume 20, Number 2, Pages 181–193 (Mi tmf3813)

Diagrammatic analysis of the fourth Legendre transform

A. N. Vasil'ev, A. K. Kazanskii, Yu. M. Pis'mak

Abstract: Analysis of the iterative solution of the equations of motion for the fourth Legendre transform shows that all graphs of the fourth transform are 4-irreducible except for an explicitly calculated four-reducible part. Knowledge of the graphs of the fourth transform is equivalent to solution of the combinatorial problem of resumming bare graphs into skeleton graphs (with respect to triple and quadruple vertices simultaneously). Explicit separation of the fourreducible part is equivalent to finding skeleton graphs responsible for overlapping effects in the equations for the triple and the quadruple vertex. The parquet approximation corresponds to neglect of all nontrivial 4-irreducible graphs of the fourth Legendre transform.

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English version:
Theoretical and Mathematical Physics, 1974, 20:2, 754–762

Citation: A. N. Vasil'ev, A. K. Kazanskii, Yu. M. Pis'mak, “Diagrammatic analysis of the fourth Legendre transform”, TMF, 20:2 (1974), 181–193; Theoret. and Math. Phys., 20:2 (1974), 754–762

Citation in format AMSBIB
\Bibitem{VasKazPis74} \by A.~N.~Vasil'ev, A.~K.~Kazanskii, Yu.~M.~Pis'mak \paper Diagrammatic analysis of the fourth Legendre transform \jour TMF \yr 1974 \vol 20 \issue 2 \pages 181--193 \mathnet{http://mi.mathnet.ru/tmf3813} \transl \jour Theoret. and Math. Phys. \yr 1974 \vol 20 \issue 2 \pages 754--762 \crossref{https://doi.org/10.1007/BF01037327} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. 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
2. 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
3. A. K. Kazanskii, “Skeleton equations with subtractions and the $R$ operation”, Theoret. and Math. Phys., 31:1 (1977), 299–305
4. V. E. Rochev, “Legendre transformations and equations for Green's functions”, Theoret. and Math. Phys., 47:2 (1981), 397–405
5. 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
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