Gauge formulation of general relativity using conformal and spin symmetries

2008 ◽  
Vol 366 (1871) ◽  
pp. 1867-1874 ◽  
Author(s):  
Charles H.-T Wang
Keyword(s):  
General Relativity ◽  
Gauge Symmetry ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Conformal Factor ◽  
Gauge Field Theories ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Free Construction ◽  
Modern Physics

The gauge symmetry inherent in Maxwell's electromagnetics has a profound impact on modern physics. Following the successful quantization of electromagnetics and other higher order gauge field theories, the gauge principle has been applied in various forms to quantize gravity. A notable development in this direction is loop quantum gravity based on the spin-gauge treatment. This paper considers a further incorporation of the conformal gauge symmetry in canonical general relativity. This is a new conformal decomposition in that it is applied to simplify recently formulated parameter-free construction of spin-gauge variables for gravity. The resulting framework preserves many main features of the existing canonical framework for loop quantum gravity regarding the spin network representation and Thiemann's regularization. However, the Barbero–Immirzi parameter is converted into the conformal factor as a canonical variable. It behaves like a scalar field but is somehow non-dynamical since the Hamiltonian constraint does not depend on its momentum. The essential steps of the mathematical derivation of this parameter-free framework for the spin-gauge variables of gravity are spelled out. The implications for the loop quantum gravity programme are briefly discussed.

scholarly journals Prelude to Simulations of Loop Quantum Gravity on Adiabatic Quantum Computers

2021 ◽  
Vol 8 ◽  
Author(s):  
Jakub Mielczarek
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Quantum Computers ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Quantum Processor ◽  
Network States ◽  
D Wave ◽  
Planck Scale Physics

The article addresses the possibility of implementing spin network states, used in the loop quantum gravity approach to Planck scale physics on an adiabatic quantum computer. The discussion focuses on applying currently available technologies and analyzes a concrete example of a D-Wave machine. It is introduced a class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states. This may inspire new generations of adiabatic quantum computers. A possibility of simulating loop quantum gravity is discussed, and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed. The presented results establish a basis for the future simulations of Planck scale physics, specifically quantum cosmological configurations, on quantum annealers.

scholarly journals FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY

2007 ◽  
Vol 16 (09) ◽  
pp. 1397-1474 ◽  
Author(s):  
MUXIN HAN ◽  
YONGGE MA ◽  
WEIMING HUANG
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Dynamics ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint ◽  
Dimensional Manifold ◽  
Fundamental Structure ◽  
Fundamental Scale

In the recent twenty 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, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

scholarly journals QUANTUM GRAVITY BY THE COMPLEX CANONICAL FORMULATION

1992 ◽  
Vol 01 (03n04) ◽  
pp. 439-523 ◽  
Author(s):  
HIDEO KODAMA
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Conventional Treatment ◽  
Quantum States ◽  
Hamiltonian Constraint ◽  
Canonical Formulation ◽  
Recent Developments ◽  
Canonical Approach ◽  
New Formulation ◽  
Basic Features

The basic features of the complex canonical formulation of general relativity and the recent developments in the quantum gravity program based on it are reviewed. The exposition is intended to be complementary to the review articles already available and some original arguments are included. In particular the conventional treatment of the Hamiltonian constraint and quantum states in the canonical approach to quantum gravity is criticized and a new formulation is proposed.

scholarly journals ENTROPY AND AREA IN LOOP QUANTUM GRAVITY

2005 ◽  
Vol 14 (12) ◽  
pp. 2301-2305
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Black Hole Entropy ◽  
Black Hole Thermodynamics ◽  
Three Dimensions ◽  
Spin Network

Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. We argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only lets that volume grow as quickly as the area bounding it.

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.

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 MULTI-PLAQUETTE SOLUTIONS FOR DISCRETIZED ASHTEKAR GRAVITY

1996 ◽  
Vol 11 (05) ◽  
pp. 349-356 ◽  
Author(s):  
KIYOSHI EZAWA
Keyword(s):  
Quantum Gravity ◽  
Heat Kernel ◽  
Gauge Theories ◽  
Hamiltonian Constraint ◽  
Spin Network ◽  
Connected Set ◽  
Network States ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll’s discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-DeWitt equation. These solutions have their support on the connected set of plaquettes. We also show that these solutions are not normalizable with respect to the induced heat-kernel measure on SL(2, C) gauge theories.

scholarly journals A quantized spacetime based on Spin(3,1) symmetry

2016 ◽  
Vol 25 (13) ◽  
pp. 1645004
Author(s):  
Pisin Chen ◽  
Hsu-Wen Chiang ◽  
Yao-Chieh Hu
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Generalized Uncertainty Principle ◽  
Spin Network ◽  
Fundamental Symmetry ◽  
New Type ◽  
Gravity Theories

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired [Formula: see text] worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where SU(2) is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds.

Corrigendum: Loop quantum gravity without the Hamiltonian constraint

2013 ◽  
Vol 30 (11) ◽  
pp. 119501 ◽  
Author(s):  
N Bodendorfer ◽  
A Stottmeister ◽  
A Thurn
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint

scholarly journals Black Holes, Gravitational Waves and Quantum Gravity

2021 ◽  
pp. 1-11
Author(s):  
W. F. Chagas-Filho
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Gravitational Waves ◽  
Loop Quantum Gravity ◽  
Canonical Quantization ◽  
Planck Length ◽  
Basic Ideas ◽  
Area And Volume

Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric quantities such as area and volume are quantized in terms of the Planck length. In this paper we present the basic ideas for a future, mathematically more rigorous, attempt to combine black holes and gravitational waves using the quantization of geometric quantities introduced by Loop Quantum Gravity.

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