Related papers: Matrix Geometry and Coherent States

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…

Persistent spin helices are a manifestation of symmetry-protected spin textures in systems with balanced spin-orbit coupling. They enable long-lived spin structures that are of interest for spintronics and coherent spin manipulation. The…

We propose a new kind of coherent state for the general $SO(D+1)$ formulation of loop quantum gravity in the $(1+D)$-dimensional space-time. Instead of Thiemann's coherent state for $SO(D+1)$ gauge theory, our coherent spin-network state is…

We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).

For a family $\mathcal{C}$ of properly embedded curves in the 2-dimensional disk $\mathbb{D}^{2}$ satisfying certain uniqueness properties, we consider convex polygons $P\subset \mathbb{D}^{2}$ and define a metric $d$ on $P$ such that…

The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes. In the classical setting, positive-definite matrices enjoy…

Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical…

We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this…

Vector coherent states (VCS) viewed as a generalization of ordinary coherent states for higher rank tensor Hilbert spaces are investigated. We consider a systematic way of generating classes of VCS which are solvable (i.e., in the present…

We illustrate the emergence of classical analogue of coherent state and its generalisation in a purely classical field theoretical setting. Our algebraic approach makes use of the Poisson bracket and symmetries of the underlying field…

We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle…

We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable…

Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphere we use the vector SU(2) coherent states…

We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum…

This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it $N$-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the $N$-bein behaves like a ``square root'' of the…

We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized…

Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…

We study the conditions for classical r-matrices to be compatible with the generalised Chern-Simons action for 3d gravity. Compatibility means solving the classical Yang-Baxter equations with a prescribed symmetric part for each of the real…