Geodesic
Integrable many body systems in the field theories
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 3, pp. 437-460 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework. They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the topological ones by the proper Hamiltonians and sources. Interpretation of the many-body dynamics as a motion on the different moduli spaces as well as the property of duality is discussed. Tower of many-body systems can be derived from a tower of the field theories with appropriate phase spaces which have a transparent interpretation in terms of the group theory. The appearance of Calogero-type systems in different physical phenomena is mentioned. 
@article{TMF_1995_103_3_a6,
     author = {A. S. Gorsky},
     title = {Integrable many body systems in the field theories},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {437--460},
     year = {1995},
     volume = {103},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a6/}
}
TY  - JOUR
AU  - A. S. Gorsky
TI  - Integrable many body systems in the field theories
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 437
EP  - 460
VL  - 103
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a6/
LA  - en
ID  - TMF_1995_103_3_a6
ER  - 
%0 Journal Article
%A A. S. Gorsky
%T Integrable many body systems in the field theories
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 437-460
%V 103
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a6/
%G en
%F TMF_1995_103_3_a6
A. S. Gorsky. Integrable many body systems in the field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 3, pp. 437-460. http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a6/

[1] F. Calogero, J. Math. Phys., 12 (1971), 419 ; J. Moser, Adv. Math., 16 (1975), 197–220 ; B. Sutherland, Phys. Rev., A5 (1972), 1372 | DOI | MR | DOI | Zbl | DOI

[2] M. Toda, Jour. Phys. Soc. Jap., 20 (1967), 431 | DOI

[3] M. Olshanetsky, A. Perelomov, Phys. Peps., 71 (1981), 313 | DOI | MR

[4] A.M. Perelomov, M.A. Olshanetsky, Phys. Rep., 94 (1983), 6 | MR

[5] D. Kazhdan, B. Kostant, S. Sternberg, Comm. on Pure and Appl. Math., XXXI (1978), 481–507 | DOI | MR | Zbl

[6] M.A. Olshanetsky, A. Perelomov, TMF, 45 (1980), 3 | MR

[7] S.N.M. Ruijsenaars, CMP, 110 (1987), 191–213 ; S.N.M. Ruijsenaars, H. Schneider, Ann. Phys., 170 (1986), 370 | MR | Zbl | DOI | MR | Zbl

[8] A. Gorsky, N. Nekrasov, Nucl. Phys., B414 (1994), 214 | MR

[9] A. Gorsky, N. Nekrasov, hep-th/9401017

[10] A. Gorsky, N. Nekrasov, hep-th/9401021

[11] N. Hitchin, Duke, Math. J., 54 (1987), 91 | MR | Zbl

[12] S. Iso, S.J. Rey, hep-th/9406192

[13] A.P. Polychronakos, Nucl. Phys., B324 (1989), 597 ; J. Leinaas, J. Myrheim, Phys. Rev., B37 (1988), 9286 ; L. Brink, T.H. Hansson, S. Konstein, M.A. Vasiliev, Nucl. Phys., B401 (1993), 591 | DOI | MR | DOI | MR | DOI | MR | Zbl

[14] N.S. Manton, PRL, 60B (1988), 191 ; M.F. Atiyah, N.S. Manton, Phys. Lett., B222 (1989), 438 | DOI | MR

[15] J. Avan, A. Jevicki, Phys. Lett., B266 (1991), 35 | DOI | MR | Zbl

[16] A. Migdal, ZHETP, 69 (1975), 810; V. Rusakov, Mod. Phys. Lett., A5 (1990), 693 ; E. Witten, preprint IASSNS-HEP-92/15; D. Gross, W. Taylor, Nucl. Phys., B400 (1993), 181 ; D. Gross, W. Taylor, Nucl. Phys., B403 (1993), 395 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[17] J.A. Minahan, A.P. Polychronakos, Phys. Lett., B302 (1993), 265 ; M. Douglas, hep-th/9409098 | DOI | MR

[18] A. Alekseev, S. Shatashvili, CMP, 128 (1990), 197 | MR | Zbl

[19] E. Witten, CMP, 144 (1992) ; J. Sonnershtein, S. Yankelowicz, Nucl. Phys., B393 (1993), 301 | MR | Zbl | MR

[20] M. Blau, G. Thompson, Nucl. Phys., B408 (1993), 345–390 ; A. Gerasimov, UUITP-16/93, hep-th/9305090 | DOI | MR | Zbl

[21] N. Nekrasov (to appear)

[22] S.N. Ruijsenaars, Integrable and superintegrable systems, eds. B. Kupershmidt, World Scientific, Singapore, 1990, 165 ; P. Freund, A. Zabrodin, CMP, 147 (1992), 277 ; O. Babelon, D. Bernard, Phys. Lett., B317 (1993), 363 | DOI | MR | MR | Zbl | DOI | MR | Zbl

[23] I. Krichever, Funk. Analiz i Prilozh., 14:4 (1980), 45 | MR | Zbl

[24] V.I. Inozemtsev, CMP, 121 (1989), 629 | MR | Zbl

[25] E. Sklyanin, Funk. Anal. Appl., 17 (1983), 273 | DOI | MR | Zbl

[26] A. Gorsky, A. Zabrodin, Journ. Phys., A26 (1993), L635 | MR | Zbl

[27] S. Ruijsenaars, CMP, 110 (1987), 191 | MR | Zbl

[28] S.N. Ruijsenaars, CMP, 115 (1988), 127 | MR | Zbl

[29] A. Alekseev, A. Malkin, CMP, 162 (1994), 147 ; A. Alekseev, hep-th/9311074 | MR | Zbl

[30] V. Fock, A. Rosly, “Moduli of flat connections and classical $r$-matrix”, ITEP-27/93

[31] A. Gorsky, V. Fock, N. Nekrasov, V. Rubtsov (to appear)

[32] L. Faddeev, S. Shatashvili, TMP, 60 (1984), 206 | MR

[33] P. Etingof, A. Kirillov, Jr., Duke, Math. Journ., 74 (1994), 585 ; P. Etingof, ; P. Etingof, I. Frenkel, A. Kirillov, ; P. Etingof, A. Kirillov, hep-th/9311132hep-th/9407047hep-th/9403168 | MR | Zbl | MR

[34] I. Cherednik, Integration of many body problems by affine $KZ$ equations, RIMS-776, 1991; A. Matsuo, Invent. Math., 1992 | MR

[35] F.D. M. Haldane, PRL, 60 (1988), 635 | DOI | MR

[36] A. Minahan, A. Polychronakos, hep-th/9309044

[37] V. Pasquier, hep-th/94005104

[38] J. Avan, M. Talon, Phys. Lett., B303 (1993), 33 ; J. Avan, O. Babelon, M. Talon, hep-th/9306102 | DOI | MR

[39] E. Sklyanin, LPTHE-93-42, hep-th/9308060

[40] G. J. Heckmann, Invent. Math., 98 (1991), 341 ; C.F. Dunkl, Trans. Amer. Math. Soc, 311 (1989) ; E.M. Opdam, Invent. Math., 98 (1989), 1 | DOI | DOI | MR | Zbl | DOI | MR | Zbl

[41] H. Airault, H. McKean, J. Moser, Comm. Pure. App. Math., 30 (1977), 95 | DOI | MR | Zbl

[42] E. Previato, In Proceedings of the Montreal Conference, 1991