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LOOP QUANTUM GRAVITY DYNAMICS: MODELS AND APPLICATIONS
Title
LOOP QUANTUM GRAVITY DYNAMICS: MODELS AND APPLICATIONS.
Creator
Vilensky, Ilya, Engle, Jonathan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
In this dissertation we study the dynamics of loop quantum gravity and its applications. We propose a tunneling phenomenon of a black hole-white hole transition and derive an amplitude for such transition using the spinfoam framework. We investigate a special class of kinematical states for loop quantum gravity - Bell spin networks - and show that their entanglement entropy obeys the area law. We develop a new spinfoam vertex amplitude that has the correct semi-classical limit. We then apply...
Show moreIn this dissertation we study the dynamics of loop quantum gravity and its applications. We propose a tunneling phenomenon of a black hole-white hole transition and derive an amplitude for such transition using the spinfoam framework. We investigate a special class of kinematical states for loop quantum gravity - Bell spin networks - and show that their entanglement entropy obeys the area law. We develop a new spinfoam vertex amplitude that has the correct semi-classical limit. We then apply this new amplitude to calculate the graviton propagator and a cosmological transition amplitude. The results of these calculations show feasibility of computations with the new amplitude and its viability as a spinfoam model. Finally, we use physical principles to radically constrain ambiguities in the cosmological dynamics and derive unique Hamiltonian dynamics for Friedmann-Robertson-Walker and Bianchi I cosmologies.
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Date Issued
2019
PURL
http://purl.flvc.org/fau/fd/FA00013349
Subject Headings
Quantum gravity, Loop quantum gravity, Cosmology, Spinfoam
Format
Document (PDF)
QUANTIZATION OF CONSTANTLY CURVED TETRAHEDRON
Title
QUANTIZATION OF CONSTANTLY CURVED TETRAHEDRON.
Creator
Hsiao, Chen-Hung, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
Quantum tetrahedron is a key building block in the theory of Loop Quantum Gravity (LQG) and plays a crucial role in the boundary states of the spinfoam amplitude of LQG. In LQG with vanishing cosmological constant, the physical Hilbert space of the quantum at tetrahedron is the 4-valent SU(2) intertwiner space labeled by irreducible representation, each assigned to a face of the quantum at tetrahedron. Furthermore, the space is the solution space of the quantum at closure condition. The area...
Show moreQuantum tetrahedron is a key building block in the theory of Loop Quantum Gravity (LQG) and plays a crucial role in the boundary states of the spinfoam amplitude of LQG. In LQG with vanishing cosmological constant, the physical Hilbert space of the quantum at tetrahedron is the 4-valent SU(2) intertwiner space labeled by irreducible representation, each assigned to a face of the quantum at tetrahedron. Furthermore, the space is the solution space of the quantum at closure condition. The area spectrum of each face of the quantum at tetrahedron is discrete and is characterized by a spin label. Classically, the correspondence between a set of solutions of at closure condition and at tetrahedron is guaranteed by the Minkowski theorem. This theorem has been generalized to the curved case, where a curved closure condition applies. The curved Minkowski theorem allows us to reconstruct homogeneously curved tetrahedra (spherical or hyperbolic tetrahedra) from a family of four SU(2) holonomies that satisfy the curved closure condition Although the quantization of the closure condition for a at tetrahedron has been extensively studied in LQG, the quantization of the curved closure condition and curved tetrahedron has not been explored yet. The homogeneously curved tetrahedron has played an important role in the recent construction of the spinfoam model with cosmological constant in 3+1 dimensional LQG. It is anticipated that the quantization of a curved tetrahedron should deFIne the building block for the boundary Hilbert space of the spinfoam model.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014446
Subject Headings
Quantum physics, Quantum theory, Quantum gravity, Tetrahedra
Format
Document (PDF)
COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS
Title
COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS.
Creator
Qu, Dongxue, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
Quantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing...
Show moreQuantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing the semiclassical consistency of LQG, because of the connection between the semiclassical approximation of path integral and the stationary phase approximation. The recent semiclassical analysis reveals the interesting relation between spinfoam amplitudes and the Regge calculus, which discretizes GR on triangulations. This relation makes the semiclassical consistency of covariant LQG promising. The spinfoam formulation also provides ways to study the n-point functions of quantum-geometry operators in LQG. Despite the novel and crucial analytic results in the spinfoam formulation, the computational complexity has been obstructed further explorations in spinfoam models. Nevertheless, numerical approaches to spinfoams open new windows to circumvent this obstruction. There has been enlightening progress on numerical computation of the spinfoam amplitudes and the two-point function. The numerical technology should expand the toolbox to investigate LQG.
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Date Issued
2022
PURL
http://purl.flvc.org/fau/fd/FA00013878
Subject Headings
Quantum gravity, Quantum theory, Quantum gravity--Mathematics, Theoretical physics
Format
Document (PDF)
DIFFEOMORPHISM INVARIANT COSMOLOGICAL SECTOR IN LOOP QUANTUM GRAVITY
Title
DIFFEOMORPHISM INVARIANT COSMOLOGICAL SECTOR IN LOOP QUANTUM GRAVITY.
Creator
Mendonca, Phillip, Engle, Jonathan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
1In this dissertation we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity,...
Show more1In this dissertation we work out in detail a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, and propose how to compare in detail the physics of this sector with that of loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. To impose the symmetry at the quantum level, on both the connection and its conjugate momentum, the method used necessarily has similiarities to the Gupta-Bleuler method of quantizing the electromagnetic field. Lastly, a strategy for embedding states of loop quantum cosmology into this new homogeneous isotropic sector, and using this embedding to compare the physics, is presented.
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Date Issued
2019
PURL
http://purl.flvc.org/fau/fd/FA00013334
Subject Headings
Diffeomorphisms, Quantum gravity, Quantum cosmology, Invariants, Isotropy
Format
Document (PDF)
Loop Quantum Gravity with Cosmological Constant
Title
Loop Quantum Gravity with Cosmological Constant.
Creator
Huang, Zichang, Han, Muxin, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The spin-foam is a covariant path-integral style approaching to the quantization of the gravity. There exist several spin-foam models of which the most successful one is the Engle-Pereira-Rovelli-Levine/Freidel-Krasnov (EPRL-FK) model. Using the EPRLFK model people are able to calculate the transition amplitude and the n-point functions of 4D geometry (both Euclidean and Lorentzian) surrounding by a given triangulated 3D geometry. The semi-classical limit of the EPRL-FK amplitude reproduces...
Show moreThe spin-foam is a covariant path-integral style approaching to the quantization of the gravity. There exist several spin-foam models of which the most successful one is the Engle-Pereira-Rovelli-Levine/Freidel-Krasnov (EPRL-FK) model. Using the EPRLFK model people are able to calculate the transition amplitude and the n-point functions of 4D geometry (both Euclidean and Lorentzian) surrounding by a given triangulated 3D geometry. The semi-classical limit of the EPRL-FK amplitude reproduces discrete classical gravity under certain assumptions, which shows that the EPRLFK model can be understood as UV completion of general relativity. On the other hand, it is very hard to dene a continuum limit and couple a cosmological constant to the EPRL-FK model. In this dissertation, we addressed the problems about continuum limit and coupling a cosmological constant to the EPRL-FK model. Followed by chapter one as a brief introduction of the loop quantum gravity and EPRL-FK model, chapter two introduces our work about demonstrating (for the first time) that smooth curved spacetime geometries satisfying Einstein equation can emerge from discrete spin-foam models under an appropriate low energy limit, which corresponds to a semi-classical continuum limit of spin-foam models. In chapter three, we bring in the cosmological constant into the spin-foam model by coupling the SL(2, C) Chern-Simons action with the EPRL action, and find that the quantum simplicity constraint is realized as the 2d surface defect in SL(2, C)Chern-Simons theory in the construction of spin-foam amplitudes. In chapter four, we present a way to describe the twisted geometry with cosmological constant whose corresponding quantum states can forms the Hilbert space of the loop quantum gravity with cosmological constant. In chapter five, we introduced a new definition of the graviton propagator, and calculate its semi-classical limit in the contents of spin-foam model with the cosmological constant. Finally the chapter six will be a outlook for my future work.
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Date Issued
2019
PURL
http://purl.flvc.org/fau/fd/FA00013218
Subject Headings
Quantum gravity, Cosmological constants, Spin foam models
Format
Document (PDF)
QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA
Title
QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA.
Creator
Dias, Rafael Guolo, Engle, Jonathan S., Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the...
Show moreWe propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014546
Subject Headings
Black holes (Astronomy), Quantum theory, Diffeomorphisms, Gravity
Format
Document (PDF)
Spin-foam dynamics of general relativity
Title
Spin-foam dynamics of general relativity.
Creator
Chaharsough Shirazi, Atousa, Engle, Jonathan S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
In this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic...
Show moreIn this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic variables in the Plebanski-Holst formulation of gravity from which spin-foam is derived are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integral in which only the Plebanski two-form appears, and in which the conne ction degrees of freedom have been integrated out. Calculating the measure factor for Plebanksi Holst formulation without the connection degrees of freedom is one of the aims of this dissertation. This analysis is at the continuum level and in order to be implemented in spin-foams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semi-classical behavior. In asymptotic analysis of the Engle-Pereira-Rovelli-Livine spin-foam model, due to the inclusion of more than the usual gravitational sector, more than the usual Regge term appears in the asymptotics of the vertex amplitude. As a consequence, solutions to the classical equations of motion of GR fail to dominate in the semi-classical limit. One solution to this problem has been proposed in which one quantum mechanically imposes restriction to a single gravitational sector, yielding what has been called the “proper” spin-foam model. However, this revised model of quantum gravity, like any proposal for a theory of quantum gravity, must pass certain tests. In the regime of small curvature, one expects a given model of quantum gravity to reproduce the predictions of the linearized theory. As a consistency check we calculate the graviton two-point function predicted by the Lorentzian proper vertex and examine its semiclassical limit.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004488, http://purl.flvc.org/fau/fd/FA00004488
Subject Headings
General relativity (Physics), Gravitation, Mass (Physics), Mathematical physics, Quantum gravity, Quantum theory
Format
Document (PDF)