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.

Fermions, loop quantum gravity and geometry

2017 ◽  
Vol 26 (11) ◽  
pp. 1750122
Author(s):  
Nabajit Chakravarty ◽  
Lipika Mullick ◽  
Pratul Bandyopadhyay
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Loop Space ◽  
Degrees Of Freedom ◽  
Deformation Parameter ◽  
Loop Quantum Gravity ◽  
Closed Loop ◽  
Time Dependent ◽  
Direction Vector ◽  
Continuous Geometry

We discuss here the geometry associated with the loop quantum gravity when it is considered to be generated from fermionic degrees of freedom. It is pointed out that a closed loop having the holonomy associated with the [Formula: see text] gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting the spin degrees of freedom. During the formation of a loop a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves [Formula: see text]-deformed gauge group [Formula: see text]. In this case, the spinorial variable attached to a node of a link is a quasispinor equipped with quasispin associated with the [Formula: see text] group. The quasispinors essentially correspond to the fermions attached to the end points of an open path in loop space. We can consider adiabatic iteration such that the quasispin associated with the [Formula: see text] group gradually evolves as the time dependent deformation parameter [Formula: see text] changes and we have the holonomy associated with the [Formula: see text] group in the limit [Formula: see text]. In this way we can have a continuous geometry developed through a sequence of [Formula: see text]-deformed holonomy-flux phase space variables which leads to a continuous gravitational field. Also it is pointed out that for a truncated general relativity given by loop quantum gravity on a fixed graph we can achieve twisted geometry and Regge geometry.

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 THE PAULI EXCLUSION PRINCIPLE AND SU(2) VERSUS SO(3) IN LOOP QUANTUM GRAVITY

2003 ◽  
Vol 12 (09) ◽  
pp. 1729-1736 ◽  
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Gauge Group ◽  
Loop Quantum Gravity ◽  
Pauli Exclusion Principle ◽  
Pauli Principle ◽  
Exclusion Principle ◽  
Spin Networks

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.

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 Loop Quantum Gravity meets Topological Phases of Matter at the Black Hole horizon

2015 ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Hans-Christian Ruiz Euler
Keyword(s):  
Quantum Gravity ◽  
Braid Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Two Dimensions ◽  
Simons Theory ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Flux Charge ◽  
Topological Quantum Computation

In this work we investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of Loop Quantum Gravity black holes by means of their relation to the braid group. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SU(2)_k-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics, since the quantum gravitational degrees of freedom of the horizon can be seen as flux-charge composites. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.

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 Quantum Holography from Fermion Fields

2021 ◽  
Vol 3 (3) ◽  
pp. 576-591
Author(s):  
Paola Zizzi
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Boundary Surface ◽  
Holographic Principle ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Fermion Fields ◽  
Planck Unit

In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

scholarly journals SELF-ORGANIZED CRITICAL BEHAVIOR: THE EVOLUTION OF FROZEN SPIN NETWORKS MODEL IN QUANTUM GRAVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 3891-3899 ◽  
Author(s):  
JIAN-ZHEN CHEN ◽  
JIAN-YANG ZHU
Keyword(s):  
Quantum Gravity ◽  
The Self ◽  
Spin Networks ◽  
Spin Network ◽  
Underlying Graph ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Propagation Rule ◽  
First Time ◽  
The Universe

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered evolution rule, the random edge model, is depending on choosing an edge randomly and changing the color of it by an even integer. Since the change of color generally violate the gauge invariance conditions imposed on the system, detailed propagation rule is needed and it can be defined in many ways. Here, we provided one new propagation rule, in which the involved even integer is not a constant one as in previous works, but changeable with certain probability. In random edge model, we do find the evolution of the system under the propagation rule exhibits power-law behavior, which is suggestive of the self-organized criticality (SOC), and it is the first time to verify the SOC behavior in such evolution model for the frozen spin network. Furthermore, the increase of the average color of the spin network in time can show the nature of inflation for the universe.

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