Related papers: Possible quantum kinematics. II. Non-minimal case
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
In this paper we study the nonlocal effects of noncommutative spacetime on simple physical systems. Our main point is the assumption that the noncommutative effects are consequences of a background field which generates a local spin…
The dissertation deals with noncommutative field theories, namely field theories compatible with the existence of a minimal (quantum gravity) length scale. Two families of quantum spacetime are considered. One is characterized by semisimple…
Starting with assumptions both simple and natural from "physical" point of view we present a direct construction of transformations preserving wide class of (anti)commutation relations which describe Euclidean/Minkowski superspace…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is…
Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
We utilize the close relation between the complex space $\textbf{C}^2$ and the real space $\textbf{R}^3$ to reformulate quantum mechanics in a manner which allows to, either or both, describe magnetic monopoles and quantize the underlying…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…
We explore a possible link between the structure of space at short length scales and the emergence of classical phenomena at macroscopic scales. To this end we adopt the paradigm of non-commutative space at short length scales and…
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems…
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…
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
The quantum oscillator and Kepler-Coulomb problems in $d$-dimensional spaces with constant curvature are analyzed from several viewpoints. In a deformed supersymmetric framework, the corresponding nonlinear potentials are shown to exhibit a…
We present a way to derive a deformation of special relativistic kinematics (possible low energy signal of a quantum theory of gravity) from the geometry of a maximally symmetric curved momentum space. The deformed kinematics is fixed (up…