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Four-dimensional quantum gravity with a cosmological constant from three-dimensional holomorphic blocks
Title
Four-dimensional quantum gravity with a cosmological constant from three-dimensional holomorphic blocks.
Creator
Haggard, Hal M., Han, Muxin, Kamiński, Wojciech, Riello, Aldo
Abstract/Description
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2, C) Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
Date Issued
2016-01
PURL
http://purl.flvc.org/fau/fd/FAUIR000021
Format
Citation
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)
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)
SYMMETRY CHARGES ON REDUCED PHASE SPACE AND ASYMPTOTIC FLATNESS
Title
SYMMETRY CHARGES ON REDUCED PHASE SPACE AND ASYMPTOTIC FLATNESS.
Creator
Tan, Hongwei, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
Though general relativity (GR) is proven to be a successful theory in describing the macroscopical nature of our universe, it still has several problems to be resolved. One of them is known as the time problem of GR. GR is a pure constraint theory, and the time evolution of the system is a gauge transformation, without carrying any physical information. One potential resolution to this issue is the relational formalism, which considers the dynamics of a material frame by coupling it to...
Show moreThough general relativity (GR) is proven to be a successful theory in describing the macroscopical nature of our universe, it still has several problems to be resolved. One of them is known as the time problem of GR. GR is a pure constraint theory, and the time evolution of the system is a gauge transformation, without carrying any physical information. One potential resolution to this issue is the relational formalism, which considers the dynamics of a material frame by coupling it to gravity. This approach allows for constructing gauge invariant observables and subsequent quantization. One realization of the relational formalism is the Brown-Kuchaˇr formalism. In this formalism, the gravity couples Brown-Kuchaˇr dust fields, and the Brown-Kuchaˇr dust fields play the roles as a family of observers. Then, one can introduce a gauge fixing scheme to the system and construct gauge invariant observables (Dirac observables) in the reduced phase Space. The probe time of the dust plays the role as the physical time of each point of the spacetime. In this thesis, we consider the Brown-Kuchaˇr formalism in an asymptotically flat background. A set of boundary conditions for the asymptotic flatness are formulated for Dirac observables on the reduced phase space. We compute the boundary term of the physical Hamiltonian, which is identical to the ADM mass. We construct a set of the symmetry charges on the reduced phase space, which encompass both the bulk terms and the boundary terms are conserved by the physical Hamiltonian evolution. The symmetry charges generate transformations preserving the asymptotically flat boundary conditions. Under the reduced-phase space Poisson bracket, the symmetry charges form an infinite dimensional Lie algebra AG after adding a central charge. A suitable quotient of AG is analogous to the BMS algebra at spatial infinity by Henneaux and Troessaert.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014398
Subject Headings
General relativity (Physics), Physics, Space and time, Spacetime
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)