Geodesic
One-loop corrections in the O(5) Skyrme model
Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 2, pp. 267-283 Cet article a éte moissonné depuis la source Math-Net.Ru

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The calculation of one-loop corrections in the Skyrme model in a curved space is considered. It is shown that the reduced system leads to the calculation of the determinant of a nondiagonal operator that acts on a space of world vector functions. A procedure is developed for calculating the Minakshisundaram–Seetey coefficients for such operators using the Balian–Bloch expansion for the Green's function in the curved space. The results show that the equivalence which holds between the Skyrme model and the Yang–Mills field at the classical level is not true at the quantum level. 
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     author = {Yu. N. Kafiev},
     title = {One-loop corrections in the {O(5)} {Skyrme} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a8/}
}
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Yu. N. Kafiev. One-loop corrections in the O(5) Skyrme model. Teoretičeskaâ i matematičeskaâ fizika, Tome 61 (1984) no. 2, pp. 267-283. http://geodesic.mathdoc.fr/item/TMF_1984_61_2_a8/

[1] Skyrme T. H. R., Proc. Roy. Soc., A260 (1961), 127 ; J. Math. Phys., 12 (1982), 1735 | DOI | MR | Zbl | DOI | MR

[2] E. Witten, Princeton Univ. Preprint, 1983 | MR

[3] Wess J., Zumino B., Phys. Lett., 37B (1971), 95 | DOI | MR

[4] Slavnov A. A., Faddeev L. D., TMF, 8:3 (1971), 297–307

[5] Arefeva I. Ya., Slavnov A. A., TMF, 44:1 (1980), 3–16 | MR

[6] Witten E., Nucl. Phys., B160 (1979), 57 | DOI | MR

[7] Gürsey F., Tze H. C., Ann. Phys., 127 (1980), 29 | DOI | MR

[8] Kafiev Yu. N., Nucl. Phys., B178 (1981), 177 | DOI | MR

[9] Felsager B., Leinaas J. M., Phys. Lett., 1980, 192 | DOI

[10] Bitar K. M., Fermi Lab. Preprint, 80/83, 1980

[11] Gutierrez W. R., Saez L. F., City College Preprint, 1982

[12] Kafiev Yu. N., Phys. Lett., 109B (1982), 43 | DOI | MR

[13] 'tHooft G., Phys. Rev., D14 (1976), 3432

[14] Belavin A. A., Polyakov A. M., Nucl. Phys., B123 (1977), 429 | DOI | MR | Zbl

[15] Duff M. J., Toms D. J., CERN preprint, TH-3259, 1982; Шварц А. С., “Эллиптические операторы и квантовая теория поля”, Совр. проблемы матем., 17, ВИНИТИ, М., 1981, 113–173 | MR | Zbl

[16] Minakshisundaram S., J. Ind. Math. Soc., 1949, 41 | MR | Zbl

[17] Balian R., Bloch C., Ann. Phys., 64 (1971), 271 | DOI | MR | Zbl

[18] Lüscher M., Symanzik K., Weisz P., Nucl. Phys., B173 (1980), 365 | DOI | MR

[19] Schild A., Phys. Rev., D16 (1977), 1722; Eguchi T., Phys. Rev. Lett., 44 (1980), 126 | DOI

[20] Faddeev L. D., Lett. Math. Phys., 1 (1976), 289 | DOI | MR

[21] Kafiev Yu. N., Nucl. Phys., B201 (1982), 341 | DOI | MR

[22] van Nieuwenhuizen P., Phys. Rep., 68 (1981), 189 ; Вейнберг С., Гравитация и космология, Мир, М., 1975 | DOI | MR

[23] Eguchi T., Gilkey P. B., Hanson A., Phys. Rep., 66 (1980), 213 | DOI | MR

[24] Seeley R. T., Proc. Symp. Pure Appl. Math., 10, AMS, 1967, 288 | DOI | MR

[25] Gilkey P. B., The Index Theorem and the Heat Equation, Publish or Perish, Boston, 1974 | MR | Zbl

[26] DeWitt B. S., Dynamical Theory of Groups and Fields, Gordon and Breach, N.-Y., 1965 | MR

[27] Lüscher M., Ann. Phys., 143 (1982), 359 | DOI | MR

[28] Gilkey P. B., J. Diff. Geom., 10 (1975), 601 | DOI | MR | Zbl

[29] Bekenstein J. D., Parker L., Phys. Rev., D23 (1981), 2850 | MR

[30] Sakai T., Tohoku Math. Jour., 23 (1971), 589 | DOI | MR | Zbl

[31] Kafiev Yu. N., Preprint TP-135, IM SO AN, Novosibirsk, 1983

[32] Grozin A. G., Preprint No 83-117, IYaF SO AN SSSR, Novosibirsk, 1983 | MR

[33] Atiyah M. F., Patodi V. K., Singer I. M., Math. Proc. Camb. Philos. Soc., 79 (1976), 71 | DOI | MR | Zbl

[34] Romanov V. N., Shvarts A. S., TMF, 41:2 (1979), 190–204 | MR