Related papers: Quantum Locally Compact Metric Spaces
Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…
We introduce the construction of induced corepresentations in the setting of locally compact quantum groups and prove that the resulting induced corepresentations are unitary under some mild integrability condition. We also establish a…
We show that countable metric spaces always have quantum isometry groups, thus extending the class of metric spaces known to possess such universal quantum-group actions. Motivated by this existence problem we define and study the notion of…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenwald-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
We introduce the coherent algebra of a compact metric measure space by analogy with the corresponding concept for a finite graph. As an application we show that upon topologizing the collection of isomorphism classes of compact metric…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
In this paper, we present a characterization of compact quantum metric spaces in terms of finite dimensional approximations. This characterization naturally leads to the introduction of a matrix analogue of a compact quantum metric space.…
We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the…
Noncommutative K\"ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous…
We briefly describe our application of a version of noncommutative differential geometry to the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$ and sketch how this might be used to determine the correct physical…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…