Thesis (M.Sc.(Natural and Agricultural Sciences)) -- University of Pretoria, 2009. / Summary in English. Includes bibliographical references (leaves 55-56).

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Thesis (M.S.)--Kent State University, 2006. / Title from PDF t.p. (viewed July 9, 2007). Advisor: Khandker Quader. Keywords: superconductor-insulator-transition, semiconductor. Includes bibliographical references (p. 69-70).

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This thesis examines the idea that when a physical theory contains symmetries, the theory should be interpreted in such a way that symmetry-related models represent the same physical state of affairs. It argues that we can best do so by drawing on analogies to ideas in philosophy of logic and language: specifically, by thinking of symmetries as a means of translating a theory into itself. It consists of six chapters, together with an introduction and conclusion. In Chapter 1, I set up the main ideas needed to more precisely frame the question at hand: namely, the notions of symmetry, interpretation, and possibility. I make some remarks about how I take these to be connected. In Chapter 2, I argue that isomorphic models should be interpreted as equivalent. After giving some motivations for doing so, I consider the main obstruction: how to provide an account of de re modality. I review how counterpart theory may be used to overcome this obstruction, and clarify how counterpart theory relates to other positions in the debate over modality de re. In Chapter 3, I show that the metaphysical debate over quidditism can be made precise by drawing on notions of translation from model theory, and argue in favour of an anti-quidditist attitude towards interpreting theories. I then consider the special case of translating a theory into itself: how such a theory should be interpreted, and what reformulations of the theory such an interpretation suggests. In Chapter 4, I turn my attention to physics. I define the notion of an internal symmetry for a theory, and argue that they may be regarded as translations from a theory into itself (in the sense of Chapter 3); and, hence, that symmetry-related models should be interpreted as equivalent. Drawing on the analogy further, I look at how the theory may be reformulated to take this interpretation into account. In Chapter 5, I look at external symmetries. I argue, drawing on ideas from Chapters 2 and 3, that models related by external symmetries should also be interpreted as equivalent. I discuss how implementing this interpretational lesson bears on finding the spacetime structure appropriate to a theory. In Chapter 6, I consider a specific external symmetry: the accelerative symmetry of Newtonian gravitation. I show that one can reformulate the theory to take this into account, setting gravitation on a spacetime structure that has absolute rotation but no absolute acceleration.

Maxwel l's equations for the vacuum are invariant under the duality rotation; however, the significance of this invariance is not well understood. The purpose of this thesis is to consider the duality rotation in greater detail than has been done previously. The duality invariance of Maxwell's equations is discussed, and it is shown that the only duality invariants bilinear in the electric and magnetic fields are arbitrary linear combinations of the components of the stress-energy-momentum tensor. It is also shown that the most general linear field transformation which leaves Maxwell's vacuum equations invariant is the duality rotation. The usual Lagrangian density for the electromagnetic field does not exhibit duality invariance. It is shown, however, that if one takes the components of the electromagnetic field tensor as field variables, then the most general Lorentz invariant Lagrangian density bilinear in the electomagnetic fields and their first derivatives is determined uniquely by the requirement of duality invariance. The ensuing field equations are identical with the iterated Maxwell equations. It is further shown that in neutrino theory the Pauli transformation of the second kind corresponds to the duality rotation. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries. / text

Copies of author's previously published works inserted. Bibliography: p. 56-57.

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