SL ( N ) : Separation of Variables for the Magnetic Chain
نویسنده
چکیده
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) of the matrix elements of T (u), so that, in the generic case, the zeros x i of B(u) are the separation coordinates and the P i = A(x i) provide their conjugate momenta. The method is illustrated with the magnetic chain and the Gaudin model, and its wider applicability is discussed.
منابع مشابه
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