Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0706.2623

Quantum Dyanmics of Loop Quantum Gravity

Muxin Han
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturbative quantum theory for the Lorentzian gravitational field on a four-dimensional manifold. In this approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of "quantum Riemannian geometry", which is discrete at a fundamental scale. In the investigation of quantum dynamics, the classical expressions of constraints are quantized as operators. The quantum evolution is contained in the solutions of the quantum constraint equations. On the other hand, the semi-classical analysis has to be carried out in order to test the semiclassical limit of the quantum dynamics. In this thesis, the structure of the dynamical theory in loop quantum gravity is presented pedagogically. The outline is as follows: first we review the classical formalism of general relativity as a dynamical theory of connections. Then the kinematical Ashtekar-Isham-Lewandowski representation is introduced as a foundation of loop quantum gravity. We discuss the construction of a Hamiltonian constraint operator and the master constraint programme, for both the cases of pure gravity and matter field coupling. Finally, some strategies are discussed concerning testing the semiclassical limit of the quantum dynamics.

Explore related subjects

gr-qchep-thmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Muxin Han. 2007-06-18. Quantum Dyanmics of Loop Quantum Gravity. https://arxiv.org/abs/0706.2623

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A class of decelerating inhomogeneous cosmological models giving rise to accelerating FLRW universes at large scales

In this manuscript, we develop a class of inhomogeneous relativistic cosmological models with the following properties: (i) They contain cosmological observers to whom the spatial geometry and the expansion are homogeneous and isotropic; (ii) Matter behaves closely to dust, as it is formed by an ensemble of massive particles whose number density $4$-vector is conserved and reacts viscously to the local tidal forces; (iii) They generalize the dust FLRW model; (iv) They give rise to effective models on large scales that reproduce the FLRW behaviour with dust and a running dark-energy term, which appears as a backreaction effect from the local gravitational potential; (v) By suitably setting the distribution of energy in the current universe, the effective large-scale equation-of-state parameter can reproduce, in principle, any polynomial on the scale factor whose term of order zero is negative; (vi) The luminous distance observations imply an apparent large-scale acceleration, as the deceleration parameter is negative, while in reality the universe is decelerating.

gr-qc↗
arXiv2026

Radial Stability of Charged Interacting Quark Stars Revisited

An error in the charged quark star literature \cite{Goncalves:2020joq} has resulted in erroneous solutions to the radial stability equations for charged interacting quark stars in \cite{zhang:2021}. In this article we recalculate the fundamental radial eigenfrequencies for charged, interacting quark stars in general relativity and discuss any departure from previous results \cite{zhang:2021}. Most of the qualitative trends persist, but the magnitudes of the separation between the maximum mass and stability points on a given branch can change significantly. We also note that all branches in \cite{zhang:2021} that contained no stable solutions now have stable solutions in their corrected counterparts. The net effect is that in all of the studied cases charged quark stars have a greater range of stability than originally predicted. We also compare four recent observational constraints not included in previous studies, and find that these constraints are satisfied by a subset of the mass-radius relations we obtain.

gr-qc↗
arXiv2026

Grey-body factor from correspondence with quasinormal mode for gravitational perturbation of higher-dimensional Reissner-Nordström black hole

We study the correspondence between quasinormal modes (QNMs) and grey-body factors (GBFs) of higher-dimensional Reissner--Nordström black holes. Considering scalar, vector, and tensor gravitational perturbations, we systematically compute the QNMs and GBFs for each spacetime dimension and set of black-hole parameters to evaluate the analytical formula connecting them. QNMs are obtained by the continued fraction and the integration-through-midpoints methods depending on the singularity structure in the Frobenius series. We compare the GBFs determined by the correspondence using QNMs with those computed numerically. The correspondence performs well for scalar($+$), vector($+$), vector($-$), and tensor perturbations. For the scalar($-$) perturbation, the GBFs obtained by the correspondence deviate noticeably from the accurate GBFs for black holes with low to intermediate values of the charge in $D>6$. The correspondence recovers reasonable accuracy at higher charges, although the effective potential exhibits double peaks, contrary to the assumption underlying the Wentzel--Kramers--Brillouin (WKB)-based derivation of the correspondence. Whereas the accuracy decreases with increasing $D$ for other perturbation types, the correspondence for the scalar($-$) perturbation yields more accurate GBFs in $D=8$ than those in $D=7$. For near-extreme black holes, the correspondence offers a reliable approximation of GBFs for the vector($-$) perturbation, even though a double-peak potential occurs in $D>6$. These results suggest that the correspondence has a wider range of applicability than might be expected from the assumption of the WKB approach.

gr-qc↗