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.

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 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 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 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 Quantum Holography from Fermion Fields

2021 ◽  
Author(s):  
Paola Zizzi
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Boundary Surface ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Fermion Fields ◽  
Planck Unit ◽  
Bogoliubov Transformations

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 Bogoliubov transformations lead to pairs of 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 Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

2021 ◽  
Author(s):  
Muxin Han ◽  
Hongguang Liu
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Late Time ◽  
White Hole ◽  
Quantum Black Hole ◽  
Effective Dynamics ◽  
Symmetric Quantum ◽  
Space Formulation

Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$. The holonomy correction in ${\bf H}_\Delta$ is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$ (which often chosen as the minimal area gap in Loop Quantum Gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\sim 1/{\Delta}^2$. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii $\sim \sqrt{\Delta}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.

scholarly journals Effective gauge group of pure loop quantum gravity is SO(3): New estimate of the Immirzi parameter

2006 ◽  
Vol 637 (1-2) ◽  
pp. 12-15 ◽  
Author(s):  
Chung-Hsien Chou ◽  
Yi Ling ◽  
Chopin Soo ◽  
Hoi-Lai Yu
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Loop Quantum Gravity

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.

Philosophy Beyond Spacetime

2021 ◽  
Keyword(s):  
Quantum Gravity ◽  
Philosophy Of Mind ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Quantum Theories ◽  
Philosophical Foundations ◽  
Naturalized Metaphysics ◽  
Theories Of Gravity ◽  
Methodological Aspects ◽  
Emergence Of Spacetime

The present volume collects essays on the philosophical foundations of quantum theories of gravity, such as loop quantum gravity and string theory. Central for philosophical concerns is quantum gravity's suggestion that space and time, or spacetime, may not exist fundamentally, but instead be a derivative entity emerging from non-spatiotemporal degrees of freedom. In the spirit of naturalized metaphysics, contributions to this volume consider the philosophical implications of this suggestion. In turn, philosophical methods and insights are brought to bear on the foundations of quantum gravity itself. For instance, the idea of functionalism, borrowed from the philosophy of mind and discussed by several chapters, exemplifies this mutual interaction the collection seeks to foster. The chapters of this collection cover three main subjects: first, the potential emergence of spacetime in various approaches to quantum gravity; second, metaphysical and epistemological considerations concerning the nature of this relation of emergence; and third, broader methodological aspects of the philosophy of quantum gravity.

scholarly journals Perturbative degrees of freedom in loop quantum gravity: anisotropies

2006 ◽  
Vol 23 (10) ◽  
pp. 3491-3516 ◽  
Author(s):  
Martin Bojowald ◽  
Héctor H Hernández ◽  
Hugo A Morales Técotl
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity
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