scholarly journals Ising spin network states for loop quantum gravity: a toy model for phase transitions

2016 ◽  
Vol 33 (6) ◽  
pp. 065005 ◽  
Author(s):  
Alexandre Feller ◽  
Etera R Livine
Keyword(s):  
Phase Transitions ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Spin Network ◽  
Ising Spin ◽  
Network States

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 Curvatures and discrete Gauss–Codazzi equation in (2 + 1)-dimensional loop quantum gravity

2015 ◽  
Vol 12 (10) ◽  
pp. 1550112
Author(s):  
Seramika Ariwahjoedi ◽  
Jusak Sali Kosasih ◽  
Carlo Rovelli ◽  
Freddy P. Zen
Keyword(s):  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Dimensional Manifold ◽  
Plane Angle ◽  
Codazzi Equation ◽  
Spin Network ◽  
3 Dimensional ◽  
Network States

We derive the Gauss–Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss–Codazzi equation for a discrete (2 + 1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2 + 1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.

scholarly journals Hidden messenger from quantum geometry: Towards information conservation in quantum gravity

2018 ◽  
Vol 33 (18) ◽  
pp. 1850103 ◽  
Author(s):  
Xiao-Kan Guo ◽  
Qing-Yu Cai
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Information Loss ◽  
Quantum Geometry ◽  
Spin Network ◽  
General Derivation ◽  
Black Hole Information ◽  
Network States ◽  
Quantum Geometries

The back reactions of Hawking radiation allow nontrivial correlations between consecutive Hawking quanta, which gives a possible way of resolving the paradox of black hole information loss known as the hidden messenger method. In a recent work of Ma et al. [ arXiv:1711.10704 ], this method is enhanced by a general derivation using small deviations of the states of Hawking quanta off canonical typicality. In this paper, we use this typicality argument to study the effects of generic back reactions on the quantum geometries described by spin network states, and discuss the viability of entropy conservation in loop quantum gravity. We find that such back reactions lead to small area deformations of quantum geometries including those of quantum black holes. This shows that the hidden-messenger method is still viable in loop quantum gravity, which is a first step towards resolving the paradox of black hole information loss in quantum gravity.

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.

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.

scholarly journals Wheeler’s it from bit proposal in loop quantum gravity

2019 ◽  
Vol 28 (10) ◽  
pp. 1950129
Author(s):  
Jarmo Mäkelä
Keyword(s):  
Phase Transition ◽  
Partition Function ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Dramatic Decrease ◽  
Spin Network ◽  
Quantum Numbers ◽  
System Of Particles ◽  
Number Formula ◽  
The Universe

As an attempt to realize Wheeler’s “it-from-bit proposal” that physics should be reduced to simple yes–no questions, we consider a model of loop quantum gravity, where the only allowed values of the quantum numbers [Formula: see text] at the punctures [Formula: see text] of the spin network on the spacelike two surfaces of spacetime are [Formula: see text] and [Formula: see text]. When [Formula: see text], the puncture is in the vacuum, and it does not contribute to the area of the two surface, whereas when [Formula: see text], the puncture is in an excited state, and the allowed values of the associated quantum number [Formula: see text] are [Formula: see text] and [Formula: see text]. As a consequence, the spin network used as a model of spacetime is analogous to a system of particles with spin [Formula: see text], and every puncture carries exactly one bit of information. When applied to spacetimes with horizon, our model enables us to find an explicit expression for the partition function of spacetime. Using this partition function we may, among other things, obtain the Bekenstein–Hawking entropy law for black holes. When applied to cosmological models with horizon, the partition function predicts a cosmic phase transition in the early universe, where the cosmological constant went through a dramatic decrease and the matter of the universe was created out of the vacuum.

scholarly journals Emergence of stringlike physics from Lorentz invariance in loop quantum gravity

2014 ◽  
Vol 23 (12) ◽  
pp. 1442023 ◽  
Author(s):  
Rodolfo Gambini ◽  
Jorge Pullin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Lorentz Invariance ◽  
Spherically Symmetric ◽  
Quantum Field ◽  
Spin Network ◽  
Symmetric Quantum

We consider a quantum field theory on a spherically symmetric quantum spacetime described by loop quantum gravity. The spin network description of spacetime in such a theory leads to equations for the quantum field that are discrete. We show that to avoid significant violations of Lorentz invariance, one needs to consider specific nonlocal interactions in the quantum field theory similar to those that appear in string theory. This is the first sign that loop quantum gravity places restrictions on the type of matter considered, and points to a connection with string theory physics.

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