Geodesic
Exact instanton-anti-instanton solutions and semiclassical expansion in the $\sigma$ model with fermions
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 60-69 
R. G. Ismagilov. Exact instanton-anti-instanton solutions and semiclassical expansion in the $\sigma$ model with fermions. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 60-69. http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a5/
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     author = {R. G. Ismagilov},
     title = {Exact instanton-anti-instanton solutions and semiclassical expansion in the~$\sigma$ model with fermions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The effective action obtained after exact integration with respect to the fermion fields is extremal on configurations that can be interpreted as instanton-anti-instanton solutions. The single-loop contribution of the obtained solutions to the functional integral is estimated.

[1] Callan C. G., Dashen R., Gross D. J., Phys. Rev., D17:6 (1978), 2717–2742

[2] Shuryak E. V., The role of instantons in QCD, Preprint 81-118, IYaF SO AN SSSR, Novosibirsk, 1981

[3] Ismagilov R. G., Franke V. A., TMF, 55:3 (1983), 401–406 | MR

[4] Dyakonov D. I., Petrov V. Yu., Instanton-based vacuum from Feynman variational principle, Preprint 900, LIYaF AN SSSR, L., 1983 | MR

[5] Witten E. A., Phys. Rev., D16:10 (1977), 2991–2994 | MR

[6] Polyakov V. M., Wiegmann P. B., Phys. Lett., 131B:1; 2; 3 (1983), 121–126 | DOI | MR

[7] Fateev V. A., Frolov I. V., Schwarz A. S., Nucl. Phys., B154:1 (1979), 1–20 | DOI

[8] Iwasaki Y., Yoshie T., Phys. Lett., 112B:4–5 (1982), 379–384 | DOI | MR