Geodesic
Ations of motion for a Legendre transform arbitrary order
Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 3, pp. 289-305 
A. N. Vasil'ev; A. K. Kazanskii. Ations of motion for a Legendre transform arbitrary order. Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 3, pp. 289-305. http://geodesic.mathdoc.fr/item/TMF_1973_14_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A study is made of the field analogs of the higher Legendre transforms introduced by de Dominieis and Martin in the framework of the functional formulation of quantum statistics [1, 2]. Equations of motion are constructed for these entities, the resulting equations being similar to the Schwinger ,equations for Green's functions.

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

[2] C. de Dominicis, P. C. Martin, J. Math. Phys., 5 (1964), 31 | DOI | MR

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

[8] R. P. Feynman, Rev. Mod. Phys., 20 (1947), 376 | MR

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

[10] A. N. Vasilev, A. K. Kazanskii, TMF, 12 (1972), 352