Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-04-20
Nucl.Phys. B709 (2005) 491-521
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, LaTeX file with amssymb; v2: Clarifications to the text, references added; v3: Minor changes, misprints corrected, o
Scientific paper
10.1016/j.nuclphysb.2004.12.016
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\{\textsf{A}, \textsf{A}^*\}\in{\cal A}$ subject to $q-$deformed Dolan-Grady relations. Using the inverse scattering method, a new family of quantum integrable models is proposed. In the simplest case, the Hamiltonian is linear in the fundamental generators of ${\cal A}$. For general values of $q$, the corresponding spectral problem is quasi-exactly solvable. Several examples of two-dimensional massive/massless (boundary) integrable models are reconsidered in light of this approach, for which the fundamental generators of ${\cal A}$ are constructed explicitly and exact results are obtained. In particular, we exhibit a dynamical Askey-Wilson symmetry algebra in the (boundary) sine-Gordon model and show that asymptotic (boundary) states can be expressed in terms of $q-$orthogonal polynomials.
No associations
LandOfFree
Deformed Dolan-Grady relations in quantum integrable models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deformed Dolan-Grady relations in quantum integrable models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformed Dolan-Grady relations in quantum integrable models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-55704