Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism

Abstract

Ruijsenaars-Schneider models associated with $A_{n-1}$ root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].

Latex file, 25 pages

References in corpus (16)

• The Calogero-Sutherland Model and Generalized Classical Polynomials
• Exact operator solution of the Calogero-Sutherland model
• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Quantum Calogero-Moser Models: Integrability for all Root Systems
• The Ruijsenaars-Schneider Model
• Elliptic quantum groups and Ruijsenaars models
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models
• Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model
• Commuting difference operators arising from the elliptic C_2^{(1)}-face model
• Elliptic Ruijsenaars-Schneider and Calogero-Moser Models Represented by Sklyanin Algebra and sl(n) Gaudin Algebra
• The Dn Ruijsenaars-Schneider model
• The dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider model
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves

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• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Explicit solution of the (quantum) elliptic Calogero-Sutherland model
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• Scalar products of the open XYZ chain with non-diagonal boundary terms
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Elliptic Ruijsenaars difference operators on bounded partitions
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms