Browsing by Subject "Quantum gravity"
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Item Aspects of cosmology and quantum gravity in an accelerating universe(2006) Krishnan, Chethan, 1978-; Fischler, WillyThe observation that we are living in a Universe that is expanding at an ever-increasing rate is a major challenge for any fundamental theory. The most obvious explanation for an accelerating Universe is a positive cosmological constant, but we do not really know how to do quantum field theory or string theory in spacetimes that are not asymptotically flat. In this thesis, we address various issues that arise in this general context. The problems we address include the stability and evolution of de Sitter-like compactifications, the possibility of defining a quantum theory in de Sitter space using quantum groups, and finally, the classical evolution of thin shells (boundaries of new phase bubbles) in an inhomogeneous Universe with positive Λ.Item Holographic complexity : bulk tests and implications(2021-05-06) Eccles, Stefan Vincent; Fischler, Willy; Caceres, Elena; Kilic, Can; Paban, Sonia; Shapiro, PaulThis dissertation consists of four chapters. The first broadly and briefly orients the reader through an introduction to holographic complexity within the AdS/CFT correspondence. The next three chapters correspond to distinct lines of research conducted during my time as a graduate student, chosen for their thematic relation to holographic complexity, and particularly the two conjectures known as "complexity equals volume" (CV), and "complexity equals action" (CA). Chapter two is based on work conducted with Josiah Couch, Willy Fischler, and Ming-Lei Xiao, studying the holographic complexity of noncommutative field theories under the CA conjecture [1]. Chapter three is based on work with Josiah Couch, Phuc Nguyen, and Ted Jacobson, studying general aspects of the CV conjecture, and addressing certain challenges to that proposal [2]. Chapter four is based on work with Elena Caceres, Josiah Couch, and Willy Fischler, testing proposed extensions of both CA and CV that apply them to subsystem complexity [3].Item In search of quantum de Sitter space: generalizing the Kodama state(2007) Randono, Andrew Culp; Matzner, Richard A. (Richard Alfred), 1942-The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi parameter. The Kodama state takes this parameter to be complex, whereas modern formulations of canonical quantum gravity require that the parameter is real. We generalize the Kodama state to real values of the Immirzi parameter, and find that the generalization opens up a large Hilbert space of states, one of which can be directly interpreted as particular slicing of de Sitter space. We then show that these states resolve, or are expected to resolve many of the problems associated with the original version of Kodama state. In order to resolve the interpretation of the multitude of states, we develop a new model of covariant classical and quantum gravity where the full Lorentz group is retained as a local symmetry group, and the canonical evolution generated by the constraints has a close relation to a larger group: that de Sitter group. This formalism gives strong evidence that the multitude of generalized Kodama states can be unified into a single quantum state that is quantum de Sitter space.Item Some considerations in the quantization of general relativity(2019-02-14) McClain, Thomas Judson, II; Matzner, Richard A. (Richard Alfred), 1942-; Dicus, Duane; Gleeson, Austin; Hazeltine, Richard; Shapiro, PaulIn this dissertation, I explore a number of topics related to the quantization of the theory of general relativity. The first chapter presents a novel algorithm for determining the sky location of a gravitational wave source. The second chapter develops a new approach to polysymplectic covariant Hamiltonian field theory, then uses that approach to produce an original quantization procedure applicable to both particles and fields. The third and final chapter applies the quantization procedure of the second chapter to the particularly challenging case of general relativity. An appendix on noise in gravitational wave detectors and a Glossary of terms are included for the convenience of the reader.Item Temporal insights from the end of space(2017-08-24) Feng, Justin Christopher; Matzner, Richard A. (Richard Alfred), 1942-; Gleeson, Austin M; Morrison, Philip J; Hazeltine, Richard D; Gompf, Robert EThis dissertation concerns the Weiss variation, its application in both classical and quantum General Relativity, and the role of spatial boundary conditions in characterizing time evolution. I review the Weiss variation in mechanics and classical field theory, and present a novel geometric derivation of the Weiss variation for the gravitational action: the Einstein-Hilbert action plus the Gibbons-Hawking-York boundary term. In particular, I use the first and second variation of area formulas (I include a derivation accessible to physicists in an appendix) to interpret and vary the Gibbons-Hawking-York boundary term. Though the Weiss variation of the gravitational action is in principle known to the relativity community, the variation of area approach formalizes the derivation, and facilitates the discussion of time evolution in General Relativity. I demonstrate the utility of the Weiss variation in quantum General Relativity by presenting a formal derivation of the Wheeler-DeWitt equation from the functional integral of quantum General Relativity by way of boundary variations. One feature of this approach is that it does not require an explicit 3+1 splitting of spacetime in the bulk. For spacetimes with spatial boundary, I show that variations in the induced metric at the spatial boundary can be used to describe time evolution--time evolution in quantum General Relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary.Item The holography of boundaries in quantum gravity(2023-06-14) Shashi, Sanjit; Cáceres, Elena; Distler, Jacques; Gordon, Cameron; Zimmerman, AaronDuality is a pervasive concept in the study of quantum gravity and string theory. One particularly profound manifestation of this idea is "holographic" duality relating quantum gravity in d+1 dimensions to quantum field theory in d dimensions, with the most concrete example being the anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. Guided by AdS/CFT, we explore the holographic interpretation of boundaries in conformal field theory. We demonstrate how various gravitational constructs and physics in AdS can be associated with specific boundary data in CFT. We also discuss some recent applications of holographic boundaries to longstanding questions in semiclassical quantum gravity regarding the black-hole information paradox and the role of Euclidean wormholes in the path integral.Item Topics in gravity(2002-05) Kashani-Poor, Amir-Kian; Fischler, WillyWe study questions relating to quantum gravity. The first part of this dissertation studies the degrees of freedom of non-commutative field theories. This class of theories presents an interesting playground for studying the UV-IR connection, a property assumed to hold in any theory of quantum gravity. To study these degrees of freedom, we submit the theories to a heat bath. We study a variety of theories with very different UV behavior. In all cases, we find indications in the non-planar sector for a reduced number of degrees of freedom at temperatures high with regard to the non-commutativity scale. Furthermore, the free energy in this sector exhibits a form which is suggestive of winding states in the spectrum. The starting point of the second part are recent astronomical observations that suggest that the universe is accelerating. Quintessence space-times have been proposed as alternative to asymptotic de Sitter spaces in order to accommodate these observations while bypassing the conceptual difficulties the latter pose for string theory. We argue that generic quintessence models that accommodate the present day acceleration tend to accelerate eternally. This implies that they exhibit horizons and hence pose the same problems for string theory as asymptotic de Sitter spaces. In the final part of this dissertation, we use open string mirror symmetry to calculate Ooguri-Vafa disk invariants of non-linear sigma models using the mirror Landau-Ginzburg theories. The target spaces we consider are the Calabi-Yau spaces obtained as the total space of the anticanonical line bundle of multiple blowups of the toric varieties P 2 and F2. Checking the integrality of the invariants requires calculating quantum corrections to the boundary variables. We show that these can be completely determined by using discrete symmetries of the superpotential of the mirror theory.Item Toward a theory of observation(2014-08) Carney, Daniel Joseph, Jr.; Fischler, Willy; Paban, SoniaQuantum mechanics is usually formulated in terms of a single Hilbert space and observables are defined as operators on this space. Attempts to describe entire spacetimes and their resident matter in this way often encounter paradoxes. For example, it has been argued that an observer falling into a black hole may be able to witness deviations from unitary, violations of semi-classical quantum field theory, and the like. This thesis argues that the essential problem is the insistence on the use of a single, global Hilbert space, because in general it may be that a physical observer cannot causally probe all of the information described by this space due to the presence of horizons. Instead, one could try to define unitary quantum physics directly in terms of the information causally accessible to particular observers. This thesis makes steps toward a systematization of this idea. Given an observer on a timelike worldline, I construct coordinates which (in good cases) cover precisely the set of events to which she can send and then receive a signal. These coordinates have spatial sections parametrized by her proper time, and the metric manifestly encodes the equivalence principle in the sense that it is flat along her worldline. To describe the quantum theory of fields according to these observers, I define Hilbert spaces in terms of field configurations on these spatial sections and show how to implement unitary time-evolution along proper time. I explain how to compare the observations of a pair of observers, and how to obtain the description according to some particular observer given some a priori global description. In this sense, the program outlined here constructs a manifestly unitary description of the events which the observer can causally probe. I give a number of explicit examples of the coordinates, and show how the quantum theory works for a uniformly accelerated observer in flat spacetime and for an inertial (co-moving) observer in an inflating universe.