Related papers: Instanton representanton of Plebanski gravity. Gra…
We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…
A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…
In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a…
For many years coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral…
We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…
In this paper we discuss a proposal of coherent states for Loop Quantum Gravity. These states are labeled by a point in the phase space of General Relativity as captured by a spin-network graph. They are defined as the gauge invariant…
In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family…
The Hilbert spaces for stable scattering states and particles are determined by the representations of the characterizing Euclidean and Poincar\'e group and given, respectively, by the square integrable functions on the momentum 2-spheres…
Holonomies of the Ashtekar-Barbero connection can be considered as abstract elements of a Lie group exponentially mapped from their connections representation. This idea provides a possibility to compare the geometric and algebraic…
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
Stable states (particles), ghosts and unstables states (particles) are discussed with respect to the time representations involved, their unitary groups and the induced Hilbert spaces. Unstable particles with their decay channels are…
We investigate a minisuperspace model of Einstein gravity plus dilaton that describes a static spherically symmetric configuration or a Kantowski - Sachs like universe. We develop the canonical formalism and identify canonical quantities…
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…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
Bilayer quantum Hall (BLQH) systems, which underlie a $U(4)$ symmetry, display unique quantum coherence effects. We study coherent states (CS) on the complex Grassmannian $\mathbb G_2^4=U(4)/U(2)^2$, orthonormal basis, $U(4)$ generators and…