We study a system of spinless electrons moving in a two-dimensional noncommutative
space subject to a perpendicular magnetic field vec B and confined by a harmonic potential …

We present examples of many-body Wigner quantum systems. The position and the
momentum operators RA and PA, A 1,..., n 1, of the particles are noncanonical and are …

We describe a quantum system consisting of a one-dimensional linear chain of n identical
harmonic oscillators coupled by a nearest neighbor interaction. Two boundary conditions …

During the last two decades quantum statistics became a field of increasing interest among
field theorists and condensed matter theorists. Various new statistics were suggested …

We consider a quantum system consisting of a one-dimensional chain of M identical
harmonic oscillators with natural frequency ω⁠, coupled by means of springs. Such systems …

By correctly identifying the role of the central extension in the centrally extended Heisenberg
algebra h⁠, we show that it is indeed possible to construct a Hopf algebraic structure on the …

We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled
by a nearest-neighbour interaction of the form (refers to the position of the rth oscillator). In …

The paper contains essentially two new results. Physically, a deformation of the
parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to …

The Wigner problem, ie the search for quantum mechanical commutation relations
consistent with the Heisenberg evolution equations of a given form is studied. In the …

An explicit construction of all finite-dimensional irreducible representations of the Lie
superalgebra in a Gel'fand–Zetlin basis is given. Particular attention is paid to the so-called …