相关论文: Quantum Curved Tetrahedron, Quantum Group Intertwi…

First a set of coherent states a la Klauder is formally constructed for the Coulomb problem in a curved space of constant curvature. Then the flat-space limit is taken to reduce the set for the radial Coulomb problem to a set of hydrogen…

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…

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…

Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…

A set of $n$ coherent states is introduced in a quantum system with $d$-dimensional Hilbert space $H(d)$. It is shown that they resolve the identity, and also have a discrete isotropy property. A finite cyclic group acts on the set of these…

In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…

The free quantum states of topologically massive electrodynamics and gravity in 2+1 dimensions, are explicitly found. It is shown that in both theories the states are described by infrared-regular polarization tensors containing a…

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In…

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…

An alternative approach introducing a 3 dimensional Ricci scalar curvature quantum operator given in terms of volume and area as well as new edge length operators is proposed. An example of monochromatic 4-valent node intertwiner state…

We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the…

In loop quantum cosmology the quantum dynamics is well understood. We approximate the full quantum dynamics in the infinite dimensional Hilbert space by projecting it on a finite dimensional submanifold thereof, spanned by suitably chosen…

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 construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…

We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the…

The convex hull on three points in two dimensional euclidean space of three flat edges (trihedron) was studied. The Bohr-Sommerfeld quantization of the area of space is performed. It is shown that it reproduces exactly the equidistant…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…

We introduce the set of framed convex polyhedra with N faces as the symplectic quotient C^2N//SU(2). A framed polyhedron is then parametrized by N spinors living in C^2 satisfying suitable closure constraints and defines a usual convex…