- PII
- S3034641X25100036-1
- DOI
- 10.7868/S3034641X25100036
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 168 / Issue number 4
- Pages
- 476-484
- Abstract
- We prove gauge equivalence between integrable field generalization of the elliptic Calogero–Moser model and the higher rank XYZ Landau–Lifshitz model of vector type on 1+1 dimensional space-time. Explicit formulae for the change of variables are derived, thus providing the Poisson map between these models.
- Keywords
- Date of publication
- 15.10.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 58
References
- 1. L. D. Landau and E. M. Lifshitz, Phys. Zs. Sowjet. 8, 153 (1935).
- 2. E. K. Sklyanin, Preprint LOMI E-3-79, Leningrad (1979).
- 3. E. K. Sklyanin, Questions of Quantum Field Theory and Statistical Physics, Part 6, Zap. Nauchn. Sem. LOMI 150, 154 (1986).
- 4. L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin (1987).
- 5. V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
- 6. V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl. 8, 226 (1974).
- 7. V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl. 13, 166 (1979).
- 8. I. Krichever, Commun. Math. Phys. 229, 229 (2002); arXiv:hep-th/0108110.
- 9. A. Levin, M. Olshanetsky, and A. Zotov, Commun. Math. Phys. 236, 93 (2003); arXiv:nlin/0110045.
- 10. A. V. Zotov and A. V. Smirnov, Theor. Math. Phys. 177, 1281 (2013).
- 11. K. Atalikov and A. Zotov, JETP Lett. 117, 630 (2023); arXiv:2303.08020 [hep-th].
- 12. R. J. Baxter, Ann. Phys. 76, 25 (1973).
- 13. F. Calogero, Lett. Nuovo Cim. 13, 411 (1975).
- 14. J. Moser, Adv. Math. 16, 1 (1975).
- 15. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep. 71, 313 (1981).
- 16. I.M. Krichever, Funct. Anal. Appl. 14, 282 (1980).
- 17. A. A. Akhmetshin, I. M. Krichever, and Y. S. Volvovski, Funct. Anal. Appl. 36, 253 (2002); arXiv:hep-th/0203192.
- 18. A. Zotov, J. Phys. A 57, 315201 (2024); arXiv:2404.01898 [hep-th].
- 19. K. Atalikov and A. Zotov, JETP Lett. 115, 757 (2022); arXiv:2204.12576 [math-ph].
- 20. M. Jimbo, T. Miwa, and M. Okado, Nucl. Phys. B 300, 74 (1988).
- 21. K. Atalikov and A. Zotov, Theoret. and Math. Phys. 219, 1004 (2024); arXiv:2403.00428 [hep-th].
- 22. K. Atalikov and A. Zotov, J. Geom. Phys. 164, 104161 (2021); arXiv:2010.14297 [hep-th].
- 23. A. G. Reiman and M. A. Semenov-Tian-Shansky, Zap. Nauchn. Sem. LOMI 150, 104 (1986).
- 24. A. V. Zotov, SIGMA 7, 067 (2011); arXiv:1012.1072 [math-ph].
- 25. A. Zabrodin and A. Zotov, JHEP 07, (2022) 023; arXiv: 2107.01697 [math-ph].
- 26. A. Belavin and V. Drinfeld, Funct. Anal. Appl. 16, (1982) 159.
- 27. A. Levin, M. Olshanetsky, and A. Zotov, JHEP 07, (2014) 012, arXiv:1405.7523 [hep-th].
- 28. A. Levin, M. Olshanetsky, and A. Zotov, J. Phys. A: Math. Theor. 49, (2016) 395202; arXiv:1603.06101 [math-ph].
- 29. M. Vasilyev and A. Zotov, Rev. Math. Phys. 31, (2019) 1930002; arXiv:1804.02777 [math-ph]
- 30. A. Zotov, Funct. Anal. Its. Appl. 59, (2025) 142; arXiv:2407.13854 [nlin.SI].
- 31. D. Domanevsky, A. Levin, M. Olshanetsky, and A. Zotov, Izvestiya: Mathematics (2026) to appear; arXiv:2501.08777 [math-ph].
- 32. A. Levin, M. Olshanetsky, and A. Zotov, Eur. Phys. J. C 82, 635 (2022); arXiv:2202.10106 [hep-th].
