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Gravitational properties of quantum bosonic stringsVazquez-Cruz, Alfredo January 1996 (has links)
No description available.
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Polymerization of 2D gravity modelsHoward, Bruce January 1998 (has links)
No description available.
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Aspects of the gauged, twisted, SL(2|1)/SL(2|1) Wess-Zumino-Novikov-Witten modelKoktava, Rachel-Louise Kvertus January 1996 (has links)
In this thesis we examine some of the interesting aspects of the Wess-Zumino- Novikov-Witten model when this model has been gauged and its energy tensor twisted by the addition of the derivative of one of its Cartan subalgebra valued currents. Specifically we consider the group valued model with the group taken as 5^(211) which is the Lie super group used to describe N = 2 supersymmetry. This model is advocated as being a good and natural description of the N = 2 superstring (also known as the charged spinning string, or N = 2 fermionic string) when it tensors an additional topological system of ghosts. The evidence for this assertion is presented by gauging and twisting the model and then extracting the N = 2 super Liouville action by the method of Hamiltonian reduction. The connection between the 5L (2|1)/5L (2|1) Wess-Zumino-Novikov-Witten model and field theory is made through its current algebra. As is true of many super groups there exists more than one interpretation of the Dynkin diagram for the algebra of 5L(2|1) and this results in more that one set of currents for this model. The classical and quantum currents in free field form are found in both cases, as is the highly non-linear transformation by which the two sets of currents are related. An analysis of a section of the cohomology of physical states of the model is undertaken. It is shown that the additional topological ghost system that tensors the gauged, twisted SL (2\l) model when it describes the N = 2 string only contributes a vacuum state to the overall cohomology, so reducing the analysis. As the 5L(2|1)/5L(2|1) Wess-Zumino-Novikov-Witten model is a topological field theory its spectrum of physical states lie in the cohomology class defined with respect to the BRST charge. The spectrum formed from the free field currents composes the so called Wakimoto module and this is calculated via the BRST formalism.
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The Microcanonical Density of States and Causal Dynamical TriangulationsThomson, Mitchell 17 February 2011 (has links)
Brown and York's gravitational microcanonical density of states is extended to general spacetime dimension and shown to be dependent upon features of the 4 dimensional gravitational action for its interpretation. Black hole entropy is calculated from the density of states path integral in general spacetime dimension, and the interpretation is shown to be likewise dependent upon the dimension of spacetime. The entropy of de Sitter and Rindler horizons are calculated using the black hole density of states and the notion of local horizon entropy density is shown to be supported. The applicability of the microcanonical ensemble to black hole mechanics is discussed at a fundamental level focussing on the absence of angular velocity as an external parameter in the gravitational Hamiltonian. The rotational ensemble and a new ensemble - the angular momentum ensemble - are introduced following Jaynes' information theory approach to statistical mechanics and proposed as more compelling candidates to calculate black hole entropy as a function of state.
A program to calculate the density of states path integral non-perturbatively using causal dynamical triangulations is initiated. Regge calculus expressions for extrinsic curvature are extended to the case of Lorentzian hypersurfaces and used to derive Regge calculus expressions for quasilocal energy-momentum. The Regge version of the black hole density of states action is derived and specialised to the 3d and 4d spacetime constructions of causal dynamical triangulations.
Finally, the recent suggestion that entropy is observer dependent is shown to be incompatible with the Tolman law for the equilibrium temperature in a gravitational field.
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Forays into Mathematical PhysicsHackett, Jonathan January 2007 (has links)
Two different works in mathematical physics are presented:
A construction of conformal infinity in null and spatial directions is constructed
for the Rainbow-flat space-time corresponding to doubly special relativity. From
this construction a definition of asymptotic DSRness is put forward which is com-
patible with the correspondence principle of Rainbow gravity. Furthermore a result
equating asymptotically flat space-times with asymptotically DSR spacetimes is
presented.
An overview of microlocality in braided ribbon networks is presented. Follow-
ing this, a series of definitions are presented to explore the concept of microlocality
and the topology of ribbon networks. Isolated substructure of ribbon networks are
introduced, and a theorem is proven that allows them to be relocated. This is fol-
lowed by a demonstration of microlocal translations. Additionally, an investigation
into macrolocality and the implications of invariants in braided ribbon networks
are presented.
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The Statistical Fingerprints of Quantum GravityAnsari, Mohammad Hossein 12 September 2008 (has links)
In this thesis some equilibrium and non-equilibrium statistical
methods are implied on two different versions of non-perturbative
quantum gravity.
Firstly, we report a novel statistical mechanics in which a class of evolutionary maps
act on trivalent spin network in randomly chosen initial states
and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated.
Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic
systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way.
Thirdly, two novel properties of area operator in
Loop Quantum Gravity are reported: 1) the generic degeneracy
and 2) the ladder symmetry. These were not known previously for years. The first one indicates that
corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of
degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly
in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly
spaced subsets, each called a `generation.' All generations are evenly
spaced; but the gap between the levels in any every generation is
unique. One application of the two new properties of area operator
have been considered here for introducing a generalized picture of
horizon whose area cells are not restricted to the subset considered
in quantum isolated horizon theory. Instead, the area cells accepts
values from the complete spectrum. Such horizon in the presence of
all elements of diffeomorphism group contains a number of degrees
of freedom independently from the bulk freedom whose logarithm
scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism
applies.
Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated
from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification
effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as
discrete brightest lines. The frequency of these modes scales with
the mass of black hole. This modification to Hawking's radiation
indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.
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Forays into Mathematical PhysicsHackett, Jonathan January 2007 (has links)
Two different works in mathematical physics are presented:
A construction of conformal infinity in null and spatial directions is constructed
for the Rainbow-flat space-time corresponding to doubly special relativity. From
this construction a definition of asymptotic DSRness is put forward which is com-
patible with the correspondence principle of Rainbow gravity. Furthermore a result
equating asymptotically flat space-times with asymptotically DSR spacetimes is
presented.
An overview of microlocality in braided ribbon networks is presented. Follow-
ing this, a series of definitions are presented to explore the concept of microlocality
and the topology of ribbon networks. Isolated substructure of ribbon networks are
introduced, and a theorem is proven that allows them to be relocated. This is fol-
lowed by a demonstration of microlocal translations. Additionally, an investigation
into macrolocality and the implications of invariants in braided ribbon networks
are presented.
|
28 |
The Statistical Fingerprints of Quantum GravityAnsari, Mohammad Hossein 12 September 2008 (has links)
In this thesis some equilibrium and non-equilibrium statistical
methods are implied on two different versions of non-perturbative
quantum gravity.
Firstly, we report a novel statistical mechanics in which a class of evolutionary maps
act on trivalent spin network in randomly chosen initial states
and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated.
Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic
systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way.
Thirdly, two novel properties of area operator in
Loop Quantum Gravity are reported: 1) the generic degeneracy
and 2) the ladder symmetry. These were not known previously for years. The first one indicates that
corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of
degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly
in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly
spaced subsets, each called a `generation.' All generations are evenly
spaced; but the gap between the levels in any every generation is
unique. One application of the two new properties of area operator
have been considered here for introducing a generalized picture of
horizon whose area cells are not restricted to the subset considered
in quantum isolated horizon theory. Instead, the area cells accepts
values from the complete spectrum. Such horizon in the presence of
all elements of diffeomorphism group contains a number of degrees
of freedom independently from the bulk freedom whose logarithm
scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism
applies.
Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated
from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification
effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as
discrete brightest lines. The frequency of these modes scales with
the mass of black hole. This modification to Hawking's radiation
indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.
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A 4d Lorentzian Spin Foam Model With Timelike SurfacesHnybida, Jeffrey January 2010 (has links)
We construct a 4d Lorentzian spin foam model capable of describing both spacelike and
timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian
FK model. Using the coherent state method we reproduce the results of the EPRL model
for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The
coherent states of spacelike/timelike triangles are found to correspond to elements of the
discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike
and timelike surfaces is quantized. A path integral for the quantum theory is defined
as a product of vertex amplitudes. The states corresponding to timelike triangles are
constructed in a basis diagonalised with respect to a noncompact generator. A derivation
of the matrix elements of the generators of SL(2,C) in this basis is provided.
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Quantum pre-geometry models for Quantum GravityFrancesco, Caravelli 29 June 2012 (has links)
In this thesis we review the status of an approach to Quantum Gravity through lattice toy
models, Quantum Graphity. In particular, we describe the two toy models introduced in the
literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with
Variable Speed of Light theories.
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