Geodesic
Transition function for the Toda chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 3, pp. 371-390 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We use the method of $\Lambda$-operators developed by Derkachov, Korchemsky, and Manashov to derive eigenfunctions for the open Toda chain. Using the diagram technique developed for these $\Lambda$-operators, we reproduce the Sklyanin measure and study the properties of the $\Lambda$-operators. This approach to the open Toda chain eigenfunctions reproduces the Gauss–Givental representation for these eigenfunctions.
Keywords: Toda chain, separation of variables, $Q$-operators. 
@article{TMF_2007_150_3_a1,
     author = {A. V. Silant'ev},
     title = {Transition function for {the~Toda} chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {371--390},
     year = {2007},
     volume = {150},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a1/}
}
TY  - JOUR
AU  - A. V. Silant'ev
TI  - Transition function for the Toda chain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 371
EP  - 390
VL  - 150
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a1/
LA  - ru
ID  - TMF_2007_150_3_a1
ER  - 
%0 Journal Article
%A A. V. Silant'ev
%T Transition function for the Toda chain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 371-390
%V 150
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a1/
%G ru
%F TMF_2007_150_3_a1
A. V. Silant'ev. Transition function for the Toda chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 3, pp. 371-390. http://geodesic.mathdoc.fr/item/TMF_2007_150_3_a1/

[1] S. Derkachov, G. Korchemsky, A. Manashov, JHEP, 07 (2003), 047 | DOI | MR

[2] E. K. Sklyanin, “The quantum Toda chain”, Nonlinear Equations in Classical and Quantum Field Theory, Proc. Semin. (Mendon and Paris, 1983–1984), Lecture Notes in Phys., 226, eds. N. Sanchez, H. DeVega, Springer, Berlin, 1985, 196–233 | DOI | MR | Zbl

[3] S. Kharchev, D. Lebedev, Lett. Math. Phys., 50 (1999), 53–77 | DOI | MR | Zbl

[4] V. Pasquier, M. Gaudin, J. Phys. A, 25 (1992), 5243–5252 | DOI | MR | Zbl

[5] M. Gutzwiller, Ann. Phys., 133 (1981), 304–331 | DOI | MR

[6] A. Gerasimov, S. Kharchev, D. Lebedev, S. Oblezin, Int. Math. Res. Notices, 2006 (2006), Article ID 96489 ; math.RT/0505310 | DOI | MR | Zbl

[7] A. Givental, “Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture”, Topics in Singularity Theory, Dedicated to V. I. Arnold on the occasion of his 60th birthday, Amer. Math. Soc. Transl., Ser. 2, 180, eds. A. Khovanskii, A. Varchenko, V. Vassiliev, AMS, Providence, RI, 1997, 103–115 | MR | Zbl

[8] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | Zbl

[9] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii. T. 2. Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, Nauka, M., 1974 | MR | Zbl

[10] S. M. Kharchev, D. R.Lebedev, Pisma v ZhETF, 71:6 (2000), 338–343 | DOI

[11] S. Kharchev, D. Lebedev, J. Phys. A, 34 (2001), 2247–2258 | DOI | MR | Zbl

[12] I. M. Gelfand, N. Ya. Vilenkin, Obobschennye funktsii. Vyp. 4. Nekotorye primeneniya garmonicheskogo analiza. Osnaschennye gilbertovy prostranstva, Fizmatgiz, M., 1961 | MR | MR | Zbl | Zbl

[13] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR | Zbl

[14] O. Babelon, Lett. Math. Phys., 65:3 (2003), 229–246 | DOI | MR | Zbl

[15] A. Gerasimov, S. Kharchev, D. Lebedev, Int. Math. Res. Not., 17 (2004), 823–854 | DOI | MR | Zbl