Geodesic
Legendre transformations and equations for Green's functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 184-197 Cet article a éte moissonné depuis la source Math-Net.Ru

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Higher Legendre transformations of the generating function of the Green's functions are used to obtain relations which have the meaning of many-particle equations. The second Legendre transformation gives two relations: the Edwards equation and the Bethe–Salpeter equation. The third Legendre transformation gives a system of three equations corresponding to the processes $3\to 1$, $3\to 2$, $3\to 3$. 
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V. E. Rochev. Legendre transformations and equations for Green's functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 184-197. http://geodesic.mathdoc.fr/item/TMF_1981_47_2_a3/

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