Geodesic
Generalized effective potential in nonlinear theories of fourth order
Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 1, pp. 26-35

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Legendre transformations are used to construct a generalized effective potential $\Gamma(\varphi,G,H,S)$ which depends on the vacuum expectation value of the field, the two- and three-point connected Green's functions $G$ and $H$, and the vacuum expectation $S=\langle0|S_{\text{cl}}|0\rangle$ of the classical action. An expansion is obtained for $\Gamma(\varphi,G,H,S)$ analogous to the loop expansion of the effective action $\Gamma(\varphi)$. 
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     author = {N. S. Ananikyan and G. K. Savvidi},
     title = {Generalized effective potential in nonlinear theories of fourth order},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {26--35},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_49_1_a1/}
}
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N. S. Ananikyan; G. K. Savvidi. Generalized effective potential in nonlinear theories of fourth order. Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 1, pp. 26-35. http://geodesic.mathdoc.fr/item/TMF_1981_49_1_a1/