Calogero–Sutherland system at a free fermion point
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 400-419 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present two ways to obtain precise expressions for the commuting Hamiltonians of the integrable system regarded as a fermionic limit of the quantum Calogero–Sutherland system as the number of particles tends to infinity with some special values of the coupling constant $\beta$. The construction is realized in the Fock space.
Keywords: Calogero–Sutherland system
Mots-clés : free fermion, boson–fermion correspondence.
@article{TMF_2020_205_3_a3,
     author = {M. G. Matushko},
     title = {Calogero{\textendash}Sutherland system at a~free fermion point},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {400--419},
     year = {2020},
     volume = {205},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a3/}
}
TY  - JOUR
AU  - M. G. Matushko
TI  - Calogero–Sutherland system at a free fermion point
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2020
SP  - 400
EP  - 419
VL  - 205
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a3/
LA  - ru
ID  - TMF_2020_205_3_a3
ER  - 
%0 Journal Article
%A M. G. Matushko
%T Calogero–Sutherland system at a free fermion point
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2020
%P 400-419
%V 205
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a3/
%G ru
%F TMF_2020_205_3_a3
M. G. Matushko. Calogero–Sutherland system at a free fermion point. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 3, pp. 400-419. http://geodesic.mathdoc.fr/item/TMF_2020_205_3_a3/

[1] D. Bernard, M. Gaudin, F. D. M. Haldane, V. Pasquier, “Yang–Baxter equation in spin chains with long range interactions”, J. Phys. A: Math. Gen., 26:20 (1993), 5219–5236 | DOI | MR

[2] Y. Kato, Y. Kuramoto, “Exact solution of the Sutherland model with arbitrary internal symmetry”, Phys. Rev. Lett., 74:7 (1995), 1222–1225, arXiv: cond-mat/9409031 | DOI

[3] C. F. Dunkl, “Differential-difference operators associated to reflection groups”, Trans. Amer. Math. Soc., 311:1 (1989), 167–183 | DOI | MR

[4] G. J. Heckman, “An elementary approach to the hypergeometric shift operators of Opdam”, Invent. Math., 103:1 (1991), 341–350 | DOI | MR

[5] A. P. Polychronakos, “Exchange operator formalism for integrable systems of particles”, Phys. Rev. Lett., 69:5 (1992), 703–705 | DOI | MR

[6] I. Andrić, A. Jevicki, H. Levine, “On the large-$N$ limit in symplectic matrix models”, Nucl. Phys. B, 215:2 (1983), 307–315 | DOI | MR

[7] H. Awata, Y. Matsuo, S. Odake, J. Shiraishi, “Collective field theory, Calogero–Sutherland model and generalized matrix models”, Phys. Lett. B, 347:1 (1995), 49–55, arXiv: hep-th/9411053 | DOI | MR

[8] H. Awata, Y. Matsuo, T. Yamamoto, “Collective field description of spin Calogero–Sutherland models”, J. Phys. A, 29:12 (1996), 3089–3098, arXiv: hep-th/9512065 | DOI | MR

[9] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Univ. Press, Oxford, 1998 | MR

[10] M. L. Nazarov, E. K. Sklyanin, “Integrable hierarchy of the quantum Benjamin–Ono equation”, SIGMA, 9 (2013), 078, 14 pp., arXiv: 1309.6464 | DOI | MR

[11] A. N. Sergeev, A. P. Veselov, “Dunkl operators at infinity and Calogero–Moser systems”, Internat. Math. Res. Notices, 2015:21 (2015), 10959–10986 | DOI | MR

[12] A. G. Abanov, P. B. Wiegmann, “Quantum hydrodynamics, the quantum Benjamin–Ono equation, and the Calogero model”, Phys. Rev. Lett., 95:7 (2005), 076402, 4 pp., arXiv: cond-mat/0504041 | DOI

[13] A. P. Polychronakos, “Waves and solitons in the continuum limit of the Calogero–Sutherland model”, Phys. Rev. Lett., 74:26 (1995), 5153–5157 | DOI | MR

[14] S. M. Khoroshkin, M. G. Matushko, “Fermionic limit of the Calogero–Sutherland system”, J. Math. Phys., 60:7 (2019), 071706, 17 pp. | DOI | MR

[15] A. K. Pogrebkov, “Bozon-fermionnoe sootvetstvie i kvantovye integriruemye i bezdispersnye modeli”, UMN, 58:5(353) (2003), 163–196 | DOI | DOI | MR | Zbl

[16] P. Rossi, “Gromov–Witten invariants of target curves via symplectic field theory”, J. Geom. Phys., 58:8 (2008), 931–941 | DOI | MR

[17] A. Alexandrov, A. Zabrodin, “Free fermions and tau-functions”, J. Geom. Phys., 67 (2013), 37–80 | DOI | MR

[18] V. G. Kac, A. K. Raina, N. Rozhkovskaya, Bombay lectures on highest weight representations of infinite dimensional Lie algebras, Advanced Series in Mathematical Physics, 29, World Sci., Singapore, 2013 | DOI | MR