Quantum relativistic Toda chain
نویسندگان
چکیده
منابع مشابه
Quantum Relativistic Toda Chain
Investigated is the quantum relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl’s q we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six-vertex R-matrix. Both independent Baxter’s Qoperators are constructed explicitly as seria over local Weyl generators. The operator-val...
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Investigated is the relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl's q we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six vertex R-matrix. Both independent Baxter's Q-operators are constructed explicitly as seria over local Weyl generators. The operator-valued wro...
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We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). We also show that the RTC is gauge equivalent to the discrete AKNS hierarchy and the unitary matrix model. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. The simple approach to the discrete RTC hierarchy based o...
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We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of “deformed Abelian integrals”. The properties of these integrals are discussed. We explain that these properties are necessary in order to provide the correct number of independent operators. The comparison with the cl...
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Four integrable symplectic maps approximating two Hamiltonian flows from the relativistic Toda hierarchy are introduced. They are demostrated to belong to the same hierarchy and to examplify the general scheme for symplectic maps on groups equiped with quadratic Poisson brackets. The initial value problem for the difference equations is solved in terms of a factorization problem in a group. Int...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2001
ISSN: 1110-757X,1687-0042
DOI: 10.1155/s1110757x01000055