Generalized Gaudin Models and Riccatians
| dc.creator | Ushveridze, A. G. | |
| dc.date | 1994-11-04 | |
| dc.date.accessioned | 2026-07-25T21:42:01Z | |
| dc.description | The systems of differential equations whose solutions coincide with Bethe ansatz solutions of generalized Gaudin models are constructed. These equations we call the {\it generalized spectral Riccati equations}, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is $R_{n_i}[z_1(λ),\ldots, z_r(λ)] = c_{n_i}(λ), \ i=1,\ldots, r$, where $R_{n_i}$ denote some homogeneous polynomials of degrees $n_i$ constructed from functional variables $z_i(λ)$ and their derivatives. It is assumed that $°\partial^k z_i(λ) = k+1$. The problem is to find all functions $z_i(λ)$ and $c_{n_i}(λ)$ satisfying the above equations under $2r$ additional constraints $P \ z_i(λ)=F_i(λ)$ and $(1-P) \ c_{n_i}(λ)=0$, where $P$ is a projector from the space of all rational functions onto the space of rational functions having their singularities at {\it a priori} given points. It turns out that this problem has solutions only for very special polynomials $R_{n_i}$ called {\it Riccatians}. There exist a one-to-one correspondence between systems of Riccatians and simple Lie algebras. Functions $c_{n_i}(λ)$ satisfying the system of equations constructed from Riccatians of the type ${\cal L}_r$ exactly coincide with eigenvalues of the Gaudin spectral problem associated with algebra ${\cal L}_r$. This result suggests that the generalized Gaudin models admit a total separation of variables. | |
| dc.description | LaTeX, 37 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9411035 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9411035 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/82031 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Generalized Gaudin Models and Riccatians | |
| dc.type | text |