Related papers: Spectral metrics on quantum projective spaces
We study the spectral metric aspects of the standard Podles sphere, which is a homogeneous space for quantum SU(2). The point of departure is the real equivariant spectral triple investigated by Dabrowski and Sitarz. The Dirac operator of…
The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…
We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect…
We show that the family of spectral triples for quantum projective spaces introduced by D'Andrea and Dabrowski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action…
This contribution is an introduction to the metric aspect of noncommutative geometry, with emphasize on the Moyal plane. Starting by questioning "how to define a standard meter in a space whose coordinates no longer commute?", we list…
Inspired by regularization in quantum field theory, we study topological and metric properties of spaces in which a cut-off is introduced. We work in the framework of noncommutative geometry, and focus on Connes distance associated to a…
We study the noncommutative geometry of the Moyal plane from a metric point of view. Starting from a non compact spectral triple based on the Moyal deformation A of the algebra of Schwartz functions on R^2, we explicitly compute Connes'…
We show that when non-commutative quantum mechanics is formulated on the Hilbert space of Hilbert-Schmidt operators (referred to as quantum Hilbert space) acting on a classical configuration space, spectral triplets as introduced by Connes…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
For a unital C*-algebra A, which is equipped with a spectral triple and an extension T of A by the compacts, we construct a family of spectral triples associated to T and depending on the two positive parameters (s,t). Using Rieffel's…
We construct spectral metric spaces for Gibbs measures on a one-sided topologically exact subshift of finite type. That is, for a given Gibbs measure we construct a spectral triple and show that Connes' corresponding pseudo-metric is a…
We explore the relation between noncommutative geometry, in the spectral triple formulation, and quantum mechanics. To this aim, we consider a dynamical theory of a noncommutative geometry defined by a spectral triple, and study its…
We study metric properties stemming from the Connes spectral distance on three types of non compact noncommutative spaces which have received attention recently from various viewpoints in the physics literature. These are the noncommutative…
Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number…
In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
In this paper, we study the properties of Connes spectral distances between quantum states under unitary transformations. We mainly focus on spectral triples with matrix algebras acting on finite dimensional Hilbert spaces via some linear…
A fundamental tool in noncommutative geometry is Connes' character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterisation of manifolds. A…
Metric noncommutative geometry, initiated by Alain Connes, has known some great recent developments under the impulsion of Rieffel and the introduction of the category of compact quantum metric spaces topologized thanks to the quantum…
Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…