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Loop Quantum Gravity with Cosmological Constant

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Date Issued:
2019
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 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.
Title: Loop Quantum Gravity with Cosmological Constant.
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Name(s): Huang, Zichang, author
Han, Muxin , Thesis advisor
Florida Atlantic University, Degree grantor
Charles E. Schmidt College of Science
Department of Physics
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2019
Date Issued: 2019
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 153 p.
Language(s): English
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 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.
Identifier: FA00013218 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2019.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Quantum gravity
Cosmological constants
Spin foam models
Held by: Florida Atlantic University Libraries
Sublocation: Digital Library
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013218
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.