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Quantum isotropy and dynamical quantum symmetry reduction
Title
Quantum isotropy and dynamical quantum symmetry reduction.
Creator
Hogan, Matthew, Beetle, Christopher, Engle, Jonathan S., Graduate College, Mendonca, P.
Abstract/Description
We give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which can be quantized, yielding a definition of a diffeomorphism-invariant, homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum cosmology, one exactly recovers isotropic loop quantum...
Show moreWe give a diffeomorphism and gauge covariant condition equivalent to homogeneity and isotropy which can be quantized, yielding a definition of a diffeomorphism-invariant, homogeneous isotropic sector of loop quantum gravity without fixing a graph. We then specialize this condition to Bianchi I cosmologies, in which case it becomes a condition for isotropy. We show how, by quantizing and imposing this condition in Bianchi I loop quantum cosmology, one exactly recovers isotropic loop quantum cosmology, including the usual ‘improved dynamics.’ We will also discuss how this reduction sheds light on which operator ordering to use when defining operators corresponding to directional Hubble rates, expansion, and shear quantities relevant for discussing the resolution of the initial singularity.
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Date Issued
2014
PURL
http://purl.flvc.org/fau/fd/FA00005821
Format
Document (PDF)
Generic isolated horizons in loop quantum gravity
Title
Generic isolated horizons in loop quantum gravity.
Creator
Beetle, Christopher, Engle, Jonathan
Date Issued
2010-11-15
PURL
http://purl.flvc.org/fau/flvc_fau_islandoraimporter_10.1088_0264-9381_27_23_235024_1632236016
Format
Citation
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)
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)
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)