Related papers: Quantum kinematics on q-deformed quantum spaces I,…
This paper is inspired by the work of J. S\'{a}ndor in 2006. In the paper, the authors establish some double inequalities involving the ratio $ \frac{\Gamma_{q}(x+1)}{ \Gamma_{q} \left( x+\frac{1}{2}\right)}$, where $\Gamma_{q}(x)$ is the…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
We discuss the physical consequences of making general phase space deformations on the minisuperspace of phantom cosmology. Based on the principle of physically equivalent descriptions in the deformed theory, we investigate for what values…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
The $h$-deformed quantum plane is a counterpart of the $q$-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the noncommutative…
We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere $SU_q (2)/U(1) $. The $SU_q (2)$-spinor harmonics are treated as coordinates of the quantum sphere. We consider the gauge theory for the quantum group…
In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix…
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…
We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth…
We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…