A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
A -representation with no quantum symmetric algebra
We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.
A unified model of phantom energy and dark matter.
A vertex operator approach for form factors of Belavin's -symmetric model and its application.
Addendum to "Generalized radical rings, unknotted biquandles, and quantum groups" (Colloq. Math. 109 (2007), 85-100)
Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus
The affine Birman-Wenzl-Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.
Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential.
Algebraic topology foundations of supersymmetry and symmetry breaking in quantum field theory and quantum gravity: a review.
Algèbres et équations non-linéaires
All linear representations of the Poincaré group up to dimension 8
Almost-graded central extensions of Lax operator algebras
Lax operator algebras constitute a new class of infinite dimensional Lie algebras of geometric origin. More precisely, they are algebras of matrices whose entries are meromorphic functions on a compact Riemann surface. They generalize classical current algebras and current algebras of Krichever-Novikov type. Lax operators for 𝔤𝔩(n), with the spectral parameter on a Riemann surface, were introduced by Krichever. In joint works of Krichever and Sheinman their algebraic structure was revealed and...
An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
An Analogue of the Classical Yang-Baxter Equation for General Algebraic Structures.
An analytic formula for the Jack polynomials.
An elementary construction on nonlinear coherent states associated to generalized Bargmann spaces.
An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.
An idempotent for a Jordanian quantum complex sphere
A new Jordanian quantum complex 4-sphere together with an instanton-type idempotent is obtained as a suspension of the Jordanian quantum group .
An infinite torus braid yields a categorified Jones-Wenzl projector
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.
Anyonic Groups
Application of linear hyperbolic PDE to linear quantum fields in curved spacetimes : especially black holes, time machines and a new semi-local vacuum concept
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...