Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · solv-int/9708007

Generating function of correlators in the sl_2 Gaudin model

E. K. Sklyanin
View original source ↗Read source document ↗Export metadata ↓

Abstract

For the sl_2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the SL_2 loop group. From the generating function a new explicit expression for the correlators is derived from which the determinant formulas for the norms of Bethe eigenfunctions due to Richardson and Gaudin are obtained.

Explore related subjects

solv-intnlin.SI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E. K. Sklyanin. 1997-08-18. Generating function of correlators in the sl_2 Gaudin model. https://doi.org/10.1023/a%3A1007585716273

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2024

Integer spin particles necessarily produce half-integer angular momentum in a simple complex and periodic Hamiltonian

Exact wave functions are is derived from an azimuthally periodic a self-consistent quantum Hamiltonian in 2+1 dimensions using both the Klein-Gordon and the Schroedinger equations. It isWe shown that, curiously, for both relativistic and non-relativistic equations, integer spin wave equations necessarily produce half-integer angular momentum in this potential. We find additionally that the higher energy, relativistic, solutions require an asymptotically free potential, while the lower energy, Schroedinger, solutions can exist in a potential that grows linearly with r. These are purely mathematical results, however we speculate on possible physical interpretations.

solv-int↗
arXiv2017

The averaging of non-local Hamiltonian structures in Whitham's method

We consider the $m$-phase Whitham's averaging method and propose a procedure of "averaging" of non-local Hamiltonian structures. The procedure is based on the existence of a sufficient number of local commuting integrals of a system and gives a Poisson bracket of Ferapontov type for the Whitham's system. The method can be considered as a generalization of the Dubrovin-Novikov procedure for the local field-theoretical brackets.

solv-int↗
arXiv2013

On two aspects of the Painleve analysis

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Backlund transformation related to the Lax pair.

solv-int↗