Related papers: Superintegrable anharmonic oscillators on N-dimens…
The ${\cal R}^2$ scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non-supersymmetric case the conformally coupled scalars belong to an $SO(1, 1+n)/SO(1+n)$ manifold, while in the…
We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N=2 supersymmetry in four-dimensional spacetime. Our results…
The explicit solvability of quantum superintegrable systems is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic…
Starting from the standard supertwistor realizations for conformally compactified N-extended Minkowski superspaces in three and four space-time dimensions, we elaborate on alternative realizations in terms of graded two-forms on the dual…
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation…
We study non-invariant Killing tensors with non-zero Nijenhuis torsion in the three-dimensional Euclidean space. Generalizing the corresponding integrable systems we construct two new families of superintegrable systems in $n$-dimensional…
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…
We clarify some properties of projective superspace by using a manifestly superconformal notation. In particular, we analyze the N=2 scalar multiplet in detail, including its action, and the propagator and its super-Schwinger parameters.…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
In this work the notion of Hamiltonian chain is presented as applied to anisotropic oscillator potentials especially defined on three and four dimensional Euclidean spaces. A Hamiltonian chain is a sequence of superintegrable Hamiltonians…
The classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces S^N, E^N and H^N are simultaneously approached starting from the Lie algebras so_k(N+1), which include a parametric dependence on the curvature…
We present a complete classification of symmetric superfluids, namely shift-symmetric and Poincar\'{e} invariant scalar field theories that have an enlarged set of classically conserved currents at leading order in derivatives. These…
An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently…
We introduce the Dunkl-Darboux III oscillator Hamiltonian in N dimensions, defined as a $\lambda-$deformation of the N-dimensional Dunkl oscillator. This deformation can be interpreted either as the introduction of a non-constant curvature…
We study two-parameter oscillator variations of the classical theorem on harmonic polynomials, associated with noncanonical oscillator representations of sl(n) and o(n). We find the condition when the homogeneous solution spaces of the…
We consider the harmonic-superspace ($HS$) system of equations that contains superfield $SYM^1_6$ constraints and equations of motion. A dynamical equation in the special $A$-frame is equivalent to the zero-curvature equation corresponding…
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems with 8- and 9-dimensional Lie algebras of first-order…
Darboux transformations of the singular harmonic oscillator are considered. Analytical expressions for the propagators are obtained, using the image method applied to formal singular propagators. Two-well and three-well families of…
The classical Kepler-Coulomb system in 3 dimensions is well known to be 2nd order superintegrable, with a symmetry algebra that closes polynomially under Poisson brackets. This polynomial closure is typical for 2nd order superintegrable…
We show that the isometries of the manifold of scalars in $N=2$ supergravity in $d=5$ space-time dimensions can be broken by the supergravity interactions. The opposite conclusion holds for the dimensionally reduced $d=4$ theories, where…