Quantization of bending flows

@article{Falqui2006QuantizationOB,
  title={Quantization of bending flows},
  author={Gregorio Falqui and Fabio Musso},
  journal={Czechoslovak Journal of Physics},
  year={2006},
  volume={56},
  pages={1143-1148}
}
  • G. Falqui, F. Musso
  • Published 3 October 2006
  • Mathematics
  • Czechoslovak Journal of Physics
We briefly review the Kapovich-Millson notion of bending flows as an integrable system on the space of polygons inR3, its connection with a specific GaudinXXX system, as well as the generalization to su(r),r>2. Then we consider the quantization problem of the set of Hamiltonians pertaining to the problem, quite naturally called bending Hamiltonians, and prove that their commutativity is preserved at the quantum level. 
View on Springer
arxiv.org
2 Citations

2 Citations

Citation Type

Citation Type

Limits of Gaudin systems: classical and quantum cases
We consider the XXX homogeneous Gaudin system with N sites, both in classical and the quantum case. In particular we show that a suitable limiting procedure for letting the poles of its Lax matrix…
Limits of Gaudin Algebras, Quantization of Bending Flows, Jucys–Murphy Elements and Gelfand–Tsetlin Bases
Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra $${U(\mathfrak {g})}$$ of a semisimple Lie algebra $${\mathfrak…

References

SHOWING 1-8 OF 8 REFERENCES
Gaudin Models and Bending Flows: a Geometrical Point of View
In this paper, we discuss the bi-Hamiltonian formulation of the (rational XXX) Gaudin models of spin–spin interaction, generalized to the case of sl(r)-valued 'spins'. We only consider the classical…
The symplectic geometry of polygons in Euclidean space
We study the symplectic geometry of moduli spaces M r of polygons with xed side lengths in Euclidean space. We show that M r has a natural structure of a complex analytic space and is…
Separation of Variables for Bi-Hamiltonian Systems
We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of…
Gaudin model, Bethe Ansatz and critical level
We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at the…
Classical Hamiltonian systems with sl(2) coalgebra symmetry and their integrable deformations
Several families of classical integrable systems with two degrees of freedom are derived from phase-space realizations of sl(2) Poisson coalgebras. As a remarkable fact, the existence of the…
Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous…
The quantum Gaudin system
AbstractIn this paper, we explicitly construct the quantum $$\mathfrak{g}\mathfrak{l}_n $$ Gaudin model for general n and for a general number N of particles. To this end, we construct a…
Separation of Variables
The review is based on the author’s papers since 1985 in which a new approach to the separation of variables (SoV) has being developed. It is argued that SoV, understood generally enough, could be…