[图书][B] Separation of variables and superintegrability: the symmetry of solvable systems

EG Kalnins, JM Kress, W Miller - 2018 - iopscience.iop.org
Separation of variables methods for solving partial differential equations are of immense
theoretical and practical importance in mathematical physics. They are the most powerful …

An algebraic geometric foundation for a classification of second-order superintegrable systems in arbitrary dimension

J Kress, K Schöbel, A Vollmer - The Journal of Geometric Analysis, 2023 - Springer
Second-order (maximally) superintegrable systems in dimensions two and three are
essentially classified. With increasing dimension, however, the non-linear partial differential …

Higher Order Quantum Superintegrability: A New “Painlevé Conjecture” Higher Order Quantum Superintegrability

I Marquette, P Winternitz - … Supersymmetry and Coherent States: A Volume …, 2019 - Springer
We review recent results on superintegrable quantum systems in a two-dimensional
Euclidean space with the following properties. They are integrable because they allow the …

Toward a classification of semidegenerate 3D superintegrable systems

MA Escobar-Ruiz, W Miller - Journal of Physics A: Mathematical …, 2017 - iopscience.iop.org
Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials
are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit …

[HTML][HTML] The dual pair Pin (2n)× osp (1| 2), the Dirac equation and the Bannai–Ito algebra

J Gaboriaud, L Vinet, S Vinet, A Zhedanov - Nuclear Physics B, 2018 - Elsevier
Abstract The Bannai–Ito algebra can be defined as the centralizer of the coproduct
embedding of osp (1| 2) in osp (1| 2)⊗ n. It will be shown that it is also the commutant of a …

Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras

I Marquette - Journal of Physics: Conference Series, 2019 - iopscience.iop.org
In recent years, progress toward the classification of superintegrable systems with higher
order integrals of motion has been made. In particular, a complete classification of all exotic …

Superintegrable systems on conformal surfaces

J Kress, K Schöbel, A Vollmer - arXiv preprint arXiv:2403.09191, 2024 - arxiv.org
We reconsider non-degenerate second order superintegrable systems in dimension two as
geometric structures on conformal surfaces. This extends a formalism developed by the …

Superintegrable systems, polynomial algebra structures and exact derivations of spectra

MF Hoque - arXiv preprint arXiv:1802.08410, 2018 - arxiv.org
Superintegrable systems are a class of physical systems which possess more conserved
quantities than their degrees of freedom. The study of these systems has a long history and …

An algebraic geometric foundation for a classification of superintegrable systems in arbitrary dimension

J Kress, K Schöbel, A Vollmer - arXiv preprint arXiv:1911.11925, 2019 - arxiv.org
Second-order superintegrable systems in dimensions two and three are essentially
classified. With increasing dimension, however, the non-linear partial differential equations …

Separations of Variables and Analytic Contractions on Two-Dimensional Hyperboloids

GS Pogosyan, A Yakhno - Physics of Particles and Nuclei, 2019 - Springer
In this review we present recent results in the field of analytical contraction of Lie algebra in
two-dimensional hyperbolic space. A complete geometric description for all possible …