Geodesic
Convexity properties of Legendre transformations (variational methods in quantum field theory)
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 43-58 
A. N. Vasil'ev; A. K. Kazanskii. Convexity properties of Legendre transformations (variational methods in quantum field theory). Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 1, pp. 43-58. http://geodesic.mathdoc.fr/item/TMF_1973_15_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that in scalar field theory Legendre transforms are convex functionals in variables that have the meaning of unconnected Green's functions. It follows, in particular, that a stationarity point of these functionals in an extremum.

[1] C. de Dominicis, P. C. Martin, J. Math. Phys., 5 (1964), 14 | DOI | MR

[2] C. de Dominicis, J. Math. Phys., 3 (1962), 983 | DOI

[3] G. Jona-Lasinio, Nuovo Cim., 34 (1964), 1790 | DOI

[4] G. Jona-Lasinio, Acta Phys. Hung., 19 (1965), 139 | DOI

[5] H. D. Dahmen, G. Jona-Lasinio, Nuovo Cim., 52A (1967), 807 | DOI

[6] H. D. Dahmen, G. Jona-Lasinio, Nuovo Cim., 62A (1969), 889 | DOI

[7] T. D. Lee, C. N. Yang, Phys. Rev., 113 (1959), 1165 ; 117 (1960), 22 | DOI | MR | Zbl | DOI | MR | Zbl

[8] J. Luttinger, J. Ward, Phys. Rev., 118 (1960), 1417 | DOI | MR | Zbl

[9] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Gostekhizdat, 1957 | MR

[10] R. P. Feynman, Rev. Mod. Phys., 20 (1847), 376 | MR

[11] S. Shveber, Vvedenie v relyativistskuyu kvantovuyu teoriyu, IL, 1963

[12] K. Symanzik, Commun. Math. Phys., 16 (1970), 48 | DOI | MR

[13] K. Symanzik, Rendiconti della scuolla Internasionalle di Fizica “Enrico Fermi” (Varenna, 1968), Acad. Press., 1969

[14] J. Schwinger, Proc. Nath. Acad. Sci., 44 (1958), 956 | DOI | MR | Zbl

[15] D. Ruelle, Nuovo Cim., 19 (1961), 356 | DOI | MR | Zbl

[16] K. Symanzik, J. Math. Phys., 7 (1966), 510 | DOI | MR

[17] E. S. Fradkin, Dissertatsiya, Tr. FIAN, 29 (1965)

[18] I. M. Gelfand, N. Ya. Vilenkin, Obobschennye funktsii, t. 4, Fizmatgiz, 1961 | MR

[19] Th. A. Maris, Lett. Nuovo Cim., 2 (1969), 821 | DOI

[20] N. M. Gugengolts, Kvantovaya teoriya sistem mnogikh tel, «Mir», 1967

[21] J. Schwinger, Proc. Nath. Acad. Sci., 37 (1951), 452 | DOI | MR | Zbl

[22] C. Bloch, Studies in Statisticarmechanics, v. III, 1965 | MR | Zbl

[23] A. N. Vasilev, A. K. Kazanskii, TMF, 12 (1972), 352 | MR

[24] A. N. Vasilev, A. K. Kazanskii, TMF, 14 (1973), 289 | MR