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

A cornerstone of the loop quantum gravity program is the fact that the phase space of general relativity on a fixed graph can be described by a product of SU(2) cotangent bundles per edge. In this paper we show how to parametrize this phase…

Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…

We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar…

We show that the quantized free relativistic point particle can be understood as a string in a Clifford space which generates the space-time coordinates through its inner product. The generating algebra is preserved by a unitary symmetry…

This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…

In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum…

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…

Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…

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…

In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and…

The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…

If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…

In this paper it is shown that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These…

We introduce the coherent-incoherent correspondence as a framework for deriving quantum thermodynamic uncertainty relations under continuous measurement in Lindblad dynamics. The coherent-incoherent correspondence establishes a mapping…

We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the…

We show that using the family of adapted K\"ahler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank-1, the obtained field $H^{corr}$ of quantum Hilbert spaces produced by geometric…

We apply De Haro's Geometric View of Theories to one of the simplest quantum systems: a spinless particle on a line and on a circle. The classical phase space M = T*Q is taken as the base of a trivial Hilbert bundle E ~ M x H, and the…

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1)…