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SIGMA 3 (2007), 013, 14 pages nlin.SI/0701040
https://doi.org/10.3842/SIGMA.2007.013
Contribution to the Vadim Kuznetsov Memorial Issue
Relativistic Toda Chain with Boundary Interaction at Root of Unity
Nikolai Iorgov a, Vladimir Roubtsov b, c, Vitaly Shadura a and Yuri Tykhyy a
a) Bogolyubov Institute for Theoretical Physics, 14b
Metrolohichna Str., Kyiv, 03143 Ukraine
b) LAREMA, Dépt. de Math. Université d'Angers,
2 bd. Lavoisier, 49045, Angers, France
c) ITEP, Moscow, 25 B. Cheremushkinskaja, 117259, Moscow, Russia
Received November 15, 2006, in final form January 03, 2007; Published online January 19, 2007
Abstract
We apply the Separation of Variables method to obtain
eigenvectors of commuting Hamiltonians in the quantum relativistic
Toda chain at a root of unity with boundary interaction.
Key words:
quantum integrable model with boundary interaction; quantum relativistic Toda chain.
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References
- Sklyanin E., Separation of variable. New trends,
Prog. Theoret. Phys. Suppl. 118 (1995), 35-60,
solv-int/9504001.
- Kharchev S., Lebedev D., Integral representation
for the eigenfunctions of quantum periodic Toda chain,
Lett. Math. Phys. 50 (1999), 53-77,
hep-th/9910265.
- Kharchev S., Lebedev D., Semenov-Tian-Shansky M.,
Unitary representations of Uq(sl(2,R)), the modular double, and
the multiparticle q-deformed Toda chains,
Comm. Math. Phys. 225 (2002), 573-609,
hep-th/0102180.
- Kuznetsov V.,
Separation of variables for the Dn type periodic Toda lattice,
J. Phys. A: Math. Gen. 30 (1997), 2127-2138,
solv-int/9701009.
- Iorgov N., Shadura V., Wave functions of the Toda chain
with boundary interactions, Theor. Math. Phys. 142
(2005), 289-305,
nlin.SI/0411002.
- Sklyanin E., Boundary conditions for
integrable quantum systems, J. Phys. A: Math. Gen. 21
(1988), 2375-2389.
- von Gehlen G., Iorgov N., Pakuliak S.,
Shadura V., Baxter-Bazhanov-Stoganov model: separation of
variables and Baxter equation, J. Phys. A: Math. Gen.
39 (2006), 7257-7282,
nlin.SI/0603028.
- Iorgov N., Eigenvectors of open Bazhanov-Stroganov quantum
chain, SIGMA 2 (2006), 019, 10 pages,
nlin.SI/0602010.
- Bazhanov V.V., Stroganov Yu.G., Chiral Potts model as a descendant
of the six-vertex model, J. Statist. Phys. 59 (1990),
799-817.
- Korepanov I.G., Hidden symmetries in the 6-vertex model of
statistical physics, Zap. Nauchn. Sem. S.-Peterburg.
Otdel. Mat. Inst. Steklov. (POMI) 215 (1994), 163-177
(English transl.: J. Math. Sci. (New York) 85 (1997),
1661-1670,
hep-th/9410066).
- Pakuliak S., Sergeev S., Quantum relativistic Toda chain at root
of unity: isospectrality, modified Q-operator and functional
Bethe ansatz, Int. J. Math. Math. Sci. 31 (2002),
513-554,
nlin.SI/0205037.
- Enriquez B., Rubtsov V., Commuting families in skew fields and
quantization of Beauville's fibrations, Duke Math. J.
82 (2003), 197-219,
math.AG/0112276.
- Sergeev S., Coefficient matrices of a quantum discrete auxiliary
linear problem, Zap. Nauchn. Sem. POMI 269 (2000), no. 16, 292-307
(in Russian).
- Babelon O., Talon M.,
Riemann surfaces, separation of variables and classical and
quantum integrability, Phys. Lett. A 312 (2003),
71-77,
hep-th/0209071.
- Kuznetsov V.B., Tsiganov A.V., Infinite series of Lie
algebras and boundary conditions for integrable systems, J.
Sov. Math. 59 (1992), 1085-1092.
- Kuznetsov V.B., Tsiganov A.V., Separation of variables for the quantum
relativistic Toda lattices, Report 94-07, Mathematical Preprint
Series, University of Amsterdam, 1994,
hep-th/9402111.
- Kuznetsov V.B.,
Jorgensen M.F., Christiansen P.L., New boundary conditions for
integrable lattices, J. Phys. A: Math. Gen. 28
(1995), 4639-4654,
hep-th/9503168.
- de Vega H.J., Gonzalez-Ruiz A.,
Boundary K-matrices for the XYZ, XXZ and XXX spin chains,
J. Phys. A: Math. Gen. 28 (1994), 6129-6141.
- Bazhanov V.V., Baxter R.J.,
Star-triangle relation for a three dimensional model, J.
Statist. Phys. 71 (1993), 839-864,
hep-th/9212050.
- Bugrij A.I., Iorgov N.Z., Shadura V.N.,
Alternative method of calculating the eigenvalues of the transfer matrix of
the t2 model for N = 2, JETP Lett. 119 (2005),
no. 2, 311-315.
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