scholarly journals New ‘phase’ of quantum gravity

2006 ◽  
Vol 364 (1849) ◽  
pp. 3375-3388 ◽  
Author(s):  
Charles H.-T Wang
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Conformal Symmetry ◽  
Quantum Geometry ◽  
Spin Networks ◽  
Gravitational Fields ◽  
The Past ◽  
New Phase

The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free (Barbero–Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero–Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.

scholarly journals Quantum Geometry II : The Mathematics of Loop Quantum Gravity Three dimensional quantum gravity

2020 ◽  
Author(s):  
J. Manuel Garcia-Islas
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Physical Theory ◽  
Loop Quantum Gravity ◽  
Three Dimensional ◽  
Point Of View ◽  
Quantum Geometry ◽  
Mathematical Task ◽  
Postgraduate Students ◽  
And Mathematics

Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and departing from such theory quantise it. General relativity describes gravity in terms of geometry. Therefore, quantising such theory must be equivalent to quantising geometry and that is what loop quantum gravity does. This sounds like a mathematical task as well. This is why in this paper we will present the mathematics of loop quantum gravity. We will do it from a mathematician point of view. This paper is intended to be an introduction to loop quantum gravity for postgraduate students of physics and mathematics. In this work we will restrict ourselves to the three dimensional case.

scholarly journals Quantum Geometry I: Basics of Loop Quantum Gravity

2019 ◽  
Vol 65 (1) ◽  
pp. 7
Author(s):  
J. Manuel García-Islas
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Point Of View ◽  
Quantum Geometry ◽  
And Mathematics ◽  
Area Of Study

General Relativity describes gravity in geometrical terms. This sug-gests that quantising such theory is the same as quantising geometry.The subject can therefore be called quantum geometry and one maythink that mathematicians are responsible of this subject. Unfortunatelymost mathematicians are not aware of this beautiful area of study. Herewe give a basic introduction to what quantum geometry means to a com-munity working in a theory known as loop quantum gravity. It is directedtowards graduate or upper students of physics and mathematics. We doit so from a point of view of a mathematician.

scholarly journals NEW SPIN FOAM MODELS OF QUANTUM GRAVITY

2005 ◽  
Vol 20 (17n18) ◽  
pp. 1305-1313
Author(s):  
A. MIKOVIĆ
Keyword(s):  
General Relativity ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Path Integral ◽  
Critical Review ◽  
Loop Quantum Gravity ◽  
Spin Networks ◽  
Spin Foam Models ◽  
Spin Foam Model ◽  
Spin Foam

We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

scholarly journals A CRITICAL ANALYSIS OF THE COSMOLOGICAL IMPLEMENTATION OF LOOP QUANTUM GRAVITY

2012 ◽  
Vol 27 (07) ◽  
pp. 1250032 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Critical Discussion ◽  
Point Of View ◽  
Graph Structure ◽  
Quantum Geometry ◽  
Cosmological Problem ◽  
New Perspective ◽  
Made In

This papers offers a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (LQG) theory. Revising recent issues in preserving SU(2) symmetry when quantizing the isotropic Universe, we trace a new perspective in approaching the cosmological problem within quantum geometry. The cosmological sector of LQG is reviewed and a critical point of view on LQC is presented. It is outlined how a polymer-like scale for quantum cosmology can be predicted from a proper fundamental graph underlying the homogeneous and isotropic continuous picture. However, such a minimum scale does not coincide with the choice made in LQC. Finally, the perspectives towards a consistent cosmological LQG model based on such a graph structure are discussed.

scholarly journals A First Approach to Loop Quantum Gravity in the Momentum Representation

2019 ◽  
pp. 1-8
Author(s):  
W. F. Chagas-Filho
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Classical System ◽  
Momentum Representation ◽  
First Order

We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations that can be interpreted as describing quantum gravity in the momentum representation.

scholarly journals On Conformally Coupled General Relativity

2018 ◽  
Vol 191 ◽  
pp. 07001
Author(s):  
Andrej Arbuzov ◽  
Boris Latosh
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Conformal Symmetry ◽  
Canonical Quantization ◽  
Coordinate Transformations ◽  
Model Based

A gravity model based on the conformal symmetry is presented. To specify the structure of the general coordinate transformations the Ogievetsky theorem is applied. The nonlinear symmetry realization approach is used. Canonical quantization is performed with the use of reparameterizationinvariant time and the Arnowitt-Deser-Misner foliation. Renormalizability of the constructed quantum gravity model is discussed.

Fermions, q-deformed diffeomorphism and the evolution of spin networks

2015 ◽  
Vol 24 (10) ◽  
pp. 1550074 ◽  
Author(s):  
L. Mullick ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Closed Loop ◽  
Direction Vector ◽  
Spin Networks ◽  
Spin Network ◽  
Diffeomorphism Invariance ◽  
Diffeomorphism Symmetry

We have considered here the emergence of diffeomorphism symmetry in quantum gravity in the framework of the quantization of a fermion. It is pointed out that a closed loop having the holonomy associated with the SU(2) gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting spin degrees of freedom which appear as SU(2) gauge bundle. During the formation of a loop, a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves q-deformed gauge group SUq(2). This gives rise to q-deformed diffeomorphism and helps to realize diffeomorphism invariance in quantum gravity through a sequence of q-deformed diffeomorphism in the limit q = 1. We can consider adiabatic iteration such that the quasispin associated with the quantum group SUq(2) gradually evolves as the time dependent deformation parameter q changes and in the limit q = 1, we achieve the standard spin. This essentially depicts the evolution of spin network as the loop is being formed and links fermionic degrees of freedom with loop quantum gravity.

scholarly journals Continuous formulation of the loop quantum gravity phase space

2013 ◽  
Vol 30 (8) ◽  
pp. 085013 ◽  
Author(s):  
Laurent Freidel ◽  
Marc Geiller ◽  
Jonathan Ziprick
Keyword(s):  
Phase Space ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Continuous Formulation
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