3. Electronic Theses and Dissertations (ETDs) - All submissions
Permanent URI for this communityhttps://wiredspace.wits.ac.za/handle/10539/45
Browse
6 results
Search Results
Item Self interaction of gluons within the M.I.T. bag model(1990) Quick, Jonathan Francis HareOne consequence of the non-abelian nature of Quantum Chromodynamic ( QCD ) gauge theory is that its gauge particles, or gluons as they are called, must be able to interact with each other. It has long been suggested that this must give rise to a complicated QCD vacuum structure, and many attempts to describe and model such a. problem can be found in the literature. Another consequence of the self-interaction or "be gluons is the effect of colour confinement, which specifies that. only colour-charge neutral objects may exist in, free space. One of the most successful models in QCD so far takes into account this confinement effect directly, by means of a phenomenological confining potential or bag. The aim of this thesis is to consider the structure ot the QCD vacuum within the confines of such a bag. (Abbreviation abstract)Item A quantum mechanical toy model for black holes(2018) Cannell, Regan WThe main aim of this dissertation is to investigate properties of the entropy of black holes. Our primary goal is to investigate the microstates of black holes. Our secondary goal is to study decoherence within the context of black holes. The methodology employed is to study simple, exactly solvable quantum models. These quantum models should serve as toy models for black holes. We consider exactly solvable quantum systems which have a non-degenerate energy spectrum. The energy levels of these quantum systems should not be equally spaced. By choosing an appropriate class of observables, we calculate the expectation values of these observables for different states within a suitably chosen ensemble. This is where the notion of quantum typicality arises. By comparing the expectation values of the chosen observable for several states within the ensemble, we discover that it is not always possible to distinguish among the several states. These findings are then generalised to the microstates of black holes, i.e. no measurement can distinguish black hole microstates. We then study the coherent and squeezed states of a simple quantum system. We deduce that even for such states, distinguishability is not possible. Finally, we study decoherence within the context of black holes. We find a simple quantum model that exhibits decoherence. We conclude that spacetime fluctuations can cause decoherence in quantum systems. Furthermore, by treating Hawking radiation as an effect of decoherence, we conclude that no information is lost in a black hole.Item Probing space-time geometry using young diagrams(2018) Nkumane, LwaziQuantum field theories and theories of gravity play an essential role in understanding nature. A dramatic recent development has been the discovery that quantum field theories are equivalent or dual to theories of quantum gravity on negatively curved spacetime. This duality goes under the name of the AdS/CFT correspondence. Sometimes the computation of certain observables in field theory are more difficult than the computation of the same observables in the theory of gravity and the opposite is also true. This makes the correspondence a powerful tool, that might provide an approach to strong coupling dynamics. We explore the AdS/CFT correspondence between type IIB string theory on asymptotically AdS5×S5 backgrounds as our gravity theory and N = 4 super Yang-Mills as our conformal field theory. We study BPS operators with bare dimension of order N2 in the field theory and identify them with BPS geometries on the gravity side of the correspondence. The dynamics of 1/2 BPS geometries are identified with gauge invariant operators constructed using a single field in the field theory, while the dynamics of 1/4 BPS geometries are identified with gauge invariant operators constructed using two fields. We find a sector of the two matrix model defined by the SU(2) sector in the field theory, that can be reduced to eigenvalue dynamics. The BPS operators in this sector are associated to solutions on the gravity side of the correspondence. We also identify the gauge invariant operators with bare dimension of order N, constructed using three fields, with 1/8 BPS giant graviton states. We count these gauge invariant operators constructed using three fields in the field theory and show that the counting of these operators is in agreement with the number of giant graviton states. We also demonstrate a correspondence between correlation functions of the field theory and the overlaps of the giant graviton wave functions. By working in terms of the eigenvalues we have managed to go from the matrix, which contains O(N2) degrees of freedom, to the eigenvalues which are O(N) degrees of freedom. Thus our work points to a significant simplification of the dynamics, something that deserves to be understood better. Another concrete result that we have achieved, is a proposal for some of the operators that are dual to the 1/4 BPS geometries. This is a genuine two matrix problem so it represents a novel extension of the understanding achieved by LLM of the 1/2 BPS geometries, constructed using a single matrix. The observables dual to new geometries have a bare dimension of O(N2). We have also considered operators with a bare dimension O(N), which are dual to 1/4 BPS giant gravitons. In this case too, we demonstrate that the eigenvalue description is useful. Almost all of the studies of the large N limit of CFT have focused on the planar limit. Here, since the operator dimensions scale as we take N →∞, we are considering large N but non-planar limits of the CFT. In these limits non-planar diagrams are not suppressed and the problem is considerably more difficult. The fact that we are able to explore this limit is concrete evidence for the power of the eigenvalue description and it suggests that a systematic treatment of large N but non-planar limits is possible.Item Emergent spacetime(2017) Mathaba, KagisoIn this dissertation we explore the connection between entanglement and geometry. Recent work in the AdS/CFT correspondence has uncovered fascinating connections between quantum information and geometry, suggesting that entanglement in the CFT results in the emergence of spacetime in the bulk . We work in the 1/2 BPS sector of the duality between N = 4 super Yang Mills on R x S3 and IIB string theory on AdS5 S5. We aim to test this connection by calculating the Renyi entropies in the presence of 1/2 BPS operators heavy enough to deform the background geometry. This allows us to calculate the entanglement of these operators via the replica trick. The Ryu-Takayanagi formula relates this calculation to a minimal surface in the dual supergravity geometry, thus allowing us to observe how the boundary entanglement affects the bulk spacetime. We build a formula to calculate correlation functions of 1/2 BPS operators on the Riemann sheet that arises from the replica trick. This is a recursive formula based on group theory techniques. We demonstrate how the formula works for light operators and discuss how it can be generalised to include heavy operators by considering symmetric groups of higher order.Item Gravitational description of the conformally invariant quantum mechanics of large matrices(2017) Hanmer, Jeffrey ThomasWe study the collective field theory of a free multi-matrix model in the radial sector, which has an emergent 1/r2 term, and take the large N limit. We show that it is possible to generate 2−d metrics with generic dependence on the collective field Lagrange multiplier (μ) and potential and which are distinguished by the choice of the potential. The Lagrange multiplier is shown to depend on an induced scale parameter after an I.R. regularization and breaks scale invariance. The collective field sl(2, R) algebras of the free Hamiltonian and a related alternative compact operator only close in the absence of μ. We point out that the broken conformal symmetry is contained in the associated metrics which suggests that they are related to a Near-AdS2 geometry. We also comment on the resemblance of these metrics to black hole solutions.Item Approximating the nucleon as a relativistic three particle system(1996) Ferrer, Philippe Alberto FriedrichThis dissertation is divided into two parts: the first part deals with the concepts of angular momentum and spin in classical mechanics and quantum mechanics and relativistic quantum mechanics and their connection with magnetic moments. In the second part, a model is set up of a relativistic three particle system, based on the previou.s.ly introduced concepts, which will serve as a template for a nucleon. The spatial component of the Lorentz invariant electrcmagnetic current is computed, and on the basis of it, the magnetic moment in the non-relativistic limit. It will be seen that the ratio -1 for the magnetic moment of the proton to the neutron will be recovered, in accordance 'with the static quark model, static QeD and very close to experiment.