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Spinfoam dynamics of general relativity
 Date Issued:
 2015
 Summary:
 In this dissertation the dynamics of general relativity is studied via the spinfoam approach to quantum gravity. Spinfoams are a proposal to compute a transition amplitude from a triangulated spacetime 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 PlebanskiHolst formulation of gravity from which spinfoam is derived are a Lorentz connection and a Lorentzalgebra valued twoform, called the Plebanski twoform. However, in the final spinfoam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski twoform alone. The spinfoam sum is therefore a discretized version of a PlebanskiHolst path integral in which only the Plebanski twoform 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 spinfoams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semiclassical behavior. In asymptotic analysis of the EnglePereiraRovelliLivine spinfoam 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 semiclassical 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” spinfoam 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 twopoint function predicted by the Lorentzian proper vertex and examine its semiclassical limit.
Title:  Spinfoam dynamics of general relativity. 
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Name(s): 
Chaharsough Shirazi, Atousa, author Engle, Jonathan S., 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:  2015  
Date Issued:  2015  
Publisher:  Florida Atlantic University  
Place of Publication:  Boca Raton, Fla.  
Physical Form:  application/pdf  
Extent:  84 p.  
Language(s):  English  
Summary:  In this dissertation the dynamics of general relativity is studied via the spinfoam approach to quantum gravity. Spinfoams are a proposal to compute a transition amplitude from a triangulated spacetime 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 PlebanskiHolst formulation of gravity from which spinfoam is derived are a Lorentz connection and a Lorentzalgebra valued twoform, called the Plebanski twoform. However, in the final spinfoam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski twoform alone. The spinfoam sum is therefore a discretized version of a PlebanskiHolst path integral in which only the Plebanski twoform 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 spinfoams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semiclassical behavior. In asymptotic analysis of the EnglePereiraRovelliLivine spinfoam 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 semiclassical 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” spinfoam 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 twopoint function predicted by the Lorentzian proper vertex and examine its semiclassical limit.  
Identifier:  FA00004488 (IID)  
Degree granted:  Dissertation (Ph.D.)Florida Atlantic University, 2015.  
Collection:  FAU Electronic Theses and Dissertations Collection  
Note(s):  Includes bibliography.  
Subject(s): 
General relativity (Physics) Gravitation Mass (Physics) Mathematical physics Quantum gravity Quantum theory 

Held by:  Florida Atlantic University Libraries  
Sublocation:  Digital Library  
Links:  http://purl.flvc.org/fau/fd/FA00004488  
Persistent Link to This Record:  http://purl.flvc.org/fau/fd/FA00004488  
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Use and Reproduction:  http://rightsstatements.org/vocab/InC/1.0/  
Host Institution:  FAU  
Is Part of Series:  Florida Atlantic University Digital Library Collections. 