Related papers: Perelomov type coherent states of SO(D + 1) in all…
This work can be considered as a continuation of our previous one (J.Phys., 26 (1993) 313), in which an explicit form of coherent states (CS) for all SU(N) groups was constructed by means of representations on polynomials. Here we extend…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
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…
In this article we further investigate the construction of graph coherent states, first introduced in [1], in the context of loop quantum gravity. We specifically investigate the possibility of defining a family of graph coherent states…
Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum,…
$\text{SO}(1, d+1)$ is the isometry group of $(d+1)$-dimensional de Sitter spacetime $\text{dS}_{d+1}$ and the conformal group of $\mathbb{R}^{d}$. This note gives a pedagogical introduction to the representation theory of $\text{SO}(1,…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
We construct an effective cosmological spin-foam model for a (2+1) dimensional spatially flat universe, discretized on a hypercubical lattice, containing both space- and time-like regions. Our starting point is the recently proposed…
We present a class of vector coherent states in the domain $D\times D\times >....\times D$ (n-copies), where $D$ is the complex unit disc, using a specific class of hermitian matrices. Further, as an example, we build vector coherent states…
We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states…
We provide a unified approach for finding the coherent states of various deformed algebras, including quadratic, Higgs and q-deformed algebras, which are relevant for many physical problems. For the non-compact cases, coherent states, which…
We provide a group theory approach to coherent states describing quantum space-time and its properties. This provides a relativistic framework for the metric of a Riemmanian space with bosonic and fermionic coordinates, its continuum and…
We consider quantum transition amplitudes, partition functions and observables for 3D spin foam models within $SU(2)$ quantum group deformation symmetry, where the deformation parameter is a complex fifth root of unity. By considering…
In the preceding paper of this series of articles we established peakedness properties of a family of coherent states that were introduced by Hall for any compact gauge group and were later generalized to gauge field theory by Ashtekar,…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
We compare the respective efficiencies of three quantization methods (group theoretical, coherent state and geometric) by quantizing the dynamics of a free massive particle in two-dimensional de Sitter space. For each case we consider the…
We study the loop representation of the quantum theory for 2+1 dimensional general relativity on a manifold, $M = {\cal T}^2 \times {\cal R}$, where ${\cal T}^2$ is the torus, and compare it with the connection representation for this…
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum. The operator is constructed in the loop representation, via a regularization procedure; it is finite,…