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Nonrelativistic conformal groups
In this work a systematic study of finite-dimensional nonrelativistic conformal groups is carried out under two complementary points of view. First, the conformal Killing equation is solved to obtainExpand
Classical Systems and Representations of (2+1) Newton-Hooke Symmetries
This paper investigates the classical and quantum elementary systems with Newton-Hoooke symmetry. A complete classification is given by explicit computation. In addition, we present an applicationExpand
Moyal quantization of 2+1‐dimensional Galilean systems
Stratonovich–Weyl kernels are constructed for some of the coadjoint orbits of the two‐dimensional extended Galilean group G(2+1). As an intermediate step, the unitary irreducible representationsExpand
Discrete derivatives and symmetries of difference equations
We show with an example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable for finding the symmetries of discrete equations. InExpand
Anyons, group theory and planar physics
Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with aExpand
On the local equivalence in a unidimensional world
The physical meaning of some semiunitary irreducible realizations of the unidimensional Poincare and Galilei groups, including time inversion, which are characteristic of a unidimensional world isExpand
Classical superintegrable SO (p, q) Hamiltonian systems
Abstract A family of superintegrable real Hamiltonian systems exhibiting SO ( p , q ) symmetry is obtained by symmetry reduction from free SU ( p , q ) integrable Hamiltonian systems. Among them weExpand
Integrable systems based on SU(p,q) homogeneous manifolds
The general theory of the separation of variables in Hamilton–Jacobi and Laplace–Beltrami equations on the SU(p,q) hyperboloid is used to introduce completely integrable Hamiltonian systems on O(p,q)Expand
Nonrelativistic conformal groups. II. Further developments and physical applications
The finite-dimensional conformal groups associated with the Galilei and (oscillating or expanding) Newton–Hooke space–time manifolds was characterized by the present authors in a recent work. ThreeExpand
The Stratonovich–Weyl correspondence for one‐dimensional kinematical groups
The Stratonovich–Weyl correspondence is a restatement of the Moyal quantization where the phase space is a manifold and where a group of transformations acts on it transitively. The first and mostExpand