Separation of Variables in the Classical Integrable SL(3) Magnetic Chain
نویسنده
چکیده
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation of variables. Though much simpler than two others, it has important relations to the quantum integrability. Separation of variables is constructed for the SL(3) magnetic chain — an example of integrable model associated to a nonhyperelliptic algebraic curve.
منابع مشابه
Separation of Variables . New Trends
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 the most universal tool to solve integrable models of the classical and quantum mechanics. It is shown that the standard construction of the action-angle variables from the poles of the Baker-Akhiezer...
متن کاملSL ( N ) : Separation of Variables for the Magnetic Chain
The Functional Bethe Ansatz (FBA) proposed by Sklyanin is a method which gives separation variables for systems for which an R-matrix is known. Previously the FBA was only known for SL(2) and SL(3) (and associated) R-matrices. In this paper I advance Sklyanin's program by giving the FBA for certain systems with SL(N) R-matrices. This is achieved by constructing rational functions A(u) and B(u) ...
متن کاملar X iv : s ol v - in t / 9 50 60 01 v 1 7 J un 1 99 5 Separation of Variables in the BC - type Gaudin Magnet ∗
The integrable system is introduced based on the Poisson rs-matrix structure. This is a generalization of the Gaudin magnet, and in SL(2) case isomorphic to the generalized Neumann model. The separation of variables is discussed for both classical and quantum case.
متن کاملA Biotechnological Perspective on The Affinity Magnetic Separation and Purification Based on Oligonucleotides
The rapidly growing field of biotechnology has created a critical need for simple, fast andhigh-throughput processes for the separation and purification of biomolecules from biologicalmatrices. In recent years, several bioseparation techniques have been proposed as advancedalternatives to the classical separation methods. These modern processes emphasize ultrahighselective and sensitive analysi...
متن کاملSeparation of Variables and Vacuum Structure of Massive N=2 Susy Qcd
We show how the method of separation of variables can be used to construct integrable models corresponding to curves describing vacuum structure of N = 2 SUSY Yang-Mills theories. In particular, we consider hyperelliptic curves of N = 2 SUSY QCD with even number of hypermultiplets with pairwise coinciding masses. We show that in the SU(3) case the curves correspond to the generalisations of the...
متن کامل