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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 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)
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)
bones of the ox
Title
The bones of the ox: how J.R.R. Tolkien's cosmology reflects ancient Near Eastern creation myths.
Creator
Dutton, Amanda M., Dorothy F. Schmidt College of Arts and Letters, Department of English
Abstract/Description
Scholars have well established the influence of the Old and Middle English, Norse, Welsh, and also Medieval Latin and Christian mythologies that influenced the writings of J.R.R. Tolkien. In particular, the mythology contained in The Silmarillion, specific the cosmology, behaves as sacred texts do in the primary world and mirrors a number of extant mythologies when they are directly compared. Several scholars have note, but as yet no one has studied in depth, the relationship between the...
Show moreScholars have well established the influence of the Old and Middle English, Norse, Welsh, and also Medieval Latin and Christian mythologies that influenced the writings of J.R.R. Tolkien. In particular, the mythology contained in The Silmarillion, specific the cosmology, behaves as sacred texts do in the primary world and mirrors a number of extant mythologies when they are directly compared. Several scholars have note, but as yet no one has studied in depth, the relationship between the cosmology the The Silmarillion to that of a number of extant ancient Near Eastern mythologies. This thesis seeks to address that gap in the scholarship by specifically exploring Tolkien's mythological creation story in relation to those of the Mesopotamian, Egyptian, and Abrahamic of the Near East. Such a comparative study reveals a number of structural and thematic parallels that attest to the complexity of Tolkien's work that and can be used to argue that his mythology can be considered as well-developed and surprisingly authentic as any of these ancient mythological traditions.
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Date Issued
2012
PURL
http://purl.flvc.org/FAU/3355562
Subject Headings
Criticism and interpretation, Criticism and interpretation, Myths in literature, Symbolism in literature, Cosmology, Middle Eastern literature, Criticism and interpretation
Format
Document (PDF)