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COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS

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Date Issued:
2022
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 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.
Title: COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS.
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Name(s): Qu, Dongxue, author
Han, Muxin, Thesis advisor
Florida Atlantic University, Degree grantor
Department of Physics
Charles E. Schmidt College of Science
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Date Created: 2022
Date Issued: 2022
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 162 p.
Language(s): English
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 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.
Identifier: FA00013878 (IID)
Degree granted: Dissertation (Ph.D.)--Florida Atlantic University, 2022.
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): Includes bibliography.
Subject(s): Quantum gravity
Quantum theory
Quantum gravity--Mathematics
Theoretical physics
Persistent Link to This Record: http://purl.flvc.org/fau/fd/FA00013878
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.