Related papers: Deformed Schrodinger symmetry on noncommutative sp…
We study N=2 supersymmetric U(1) gauge theory in non(anti)commutative N=2 harmonic superspace with the chirality preserving non-singlet deformation parameter. By solving the Wess-Zumino gauge preserving conditions for the analytic…
We investigate a non-trivial extension of the $D-$dimensional Poincar\'e algebra. Matrix representations are obtained. The bosonic multiplets contain antisymmetric tensor fields. It turns out that this symmetry acts in a natural geometric…
We consider the $(1 + 3)$-dimensional Einstein equations with negative cosmological constant coupled to a spherically-symmetric, massless scalar field and study perturbations around the Anti-de Sitter spacetime. We derive the resonant…
Starting from a standard noncommutative gauge theory and using the Seiberg-Witten map we propose a new version of a noncommutative gravity. We use consistent deformation theory starting from a free gauge action and gauging a killing…
We show that the asymptotic symmetry algebra of geometries with Schrodinger isometry in any dimension is an infinite dimensional algebra containing one copy of Virasoro algebra. It is compatible with the fact that the corresponding…
Exploring the concept of the extended Galilei group G. Representations for field theories in a symplectic manifold have been derived in association with the method of the Wigner function. The representation is written in the light-cone of a…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
The bound-state solutions and the su(1,1) description of the $d$-dimensional radial harmonic oscillator, the Morse and the $D$-dimensional radial Coulomb Schr\"odinger equations are reviewed in a unified way using the point canonical…
The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic…
Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter…
By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a…
We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle…
We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position…
We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…
The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the…
We demonstrate that a non self-adjoint Hamiltonian of harmonic oscillator type defined on a two-dimensional noncommutative space can be diagonalized exactly by making use of pseudo-bosonic operators. The model admits an antilinear symmetry…
We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…
We show that a class of nonrelativistic algebras including non centrally-extended Schrodinger algebra and Galilean Conformal Algebra (GCA) has an affine extension in 2+1 hitherto unknown. This extension arises out of the conformal…