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The work presented in this thesis is centred on the generation of superimposed optical fields which each carry orbital angular momentum (OAM) and the development of OAM measurement techniques. Optical fields which carry OAM have found applications ranging from optical tweezing to quantum cryptography. Due to the fact that they offer a potentially infinite-dimensional state space, much interest has been generated in the measurement of OAM in optical fields, in order for higher-dimensional quantum information processing to be realised. In this study we generate superpositions of higher-order Bessel beams and show that even though we can create a field which carries no overall OAM, we can still witness an angular rotation in the intensity profile of the beam. We also develop two new OAM measurement techniques: (1) a robust odd-even-OAM interferometer and (2) a method to measure the OAM density of an optical field by means of a single spatial light modulator (SLM). In the first chapter we give an overview of the literature regarding optical OAM, followed by the derivation of the Helmholtz wave equation from Maxwell’s equations. We illustrate that helically-phased beams, having a phase factor of exp(ilθ), possess a well-defined OAM. Definitions for the fundamental Gaussian mode, as well as two OAM-carrying modes: Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) modes are also given. Since a majority of this thesis involves generating superimposed OAM fields as well as the measurement of OAM, chapter 2 contains detailed discussions on the optical components used to generate and measure OAM. In section 2.9 we present one of our contributions to the field of OAM-measurement, which involves a stable Dove-prism embedded Mach-Zehnder interferometer, capable of sorting 41 OAM states into odd and even ports with a contrast ranging from 92% to 61%. We implement the Dove prism embedded Mach-Zehnder interferometer to mimic an amplitude damping channel for OAM states in chapter 3. Our device is useful in modelling a ‘lossy’ environment for OAM states. In chapter 4 we develop a new technique for the generation of superimposed Bessel beams through the use of a single digital hologram and theoretically and experimentally show that even though the superimposed Bessel beams can be constructed to produce no overall OAM, a rotation in the beam’s intensity profile is still present, as the field propagates. This rotation is due to the differing longitudinal wave-vectors present in the field and we make quantitative, experimental measurements of the angular rotation rates, which are in very good agreement with our theoretical predictions. We also show that the far-field of these superimposed Bessel beams, exhibit no rotation in their intensity profile and we offer a theoretical explanation for this occurrence. In chapter 5, we adapt our technique for generating superimposed Bessel beams to create non-diffracting speckle fields, which are known to possess optical vortices, and show that by controlling the standard deviation of the phase distribution within the digital hologram, we are able to control the evolution of the non-diffracting speckle field into a non-diffracting zero-order Bessel beam. Our final chapter contains a novel technique for the measurement of the OAM density of optical fields, by implementing two optical components: an SLM and a lens. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.

In this thesis we investigate the role played by fundamental properties of QED in determining the non-perturbative fermion-boson vertex. These key features are gauge invariance and multiplicative renormalisability. We use the Schwinger-Dyson equations as the non- perturbative tool to study the general structure of the fermion-boson vertex in QED. These equations, being an infinite set, have to be truncated if they are to be solved. Such a truncation is made possible by choosing a suitable non-perturbative ansatz for the fermion-boson vertex. This choice must satisfy these key properties of gauge invariance and multiplicative renormalisability. In this thesis we develop the constraints, in the case of massless unquenched QED, that have to be fulfilled to ensure that both the fermion and photon propagators are multiplicatively renormalisable-at least as far as leading and subleading logarithms are concerned. To this end, the Schwinger-Dyson equations are solved perturbatively for the fermion and photon wave-function renormalisations. We then deduce the conditions imposed by multiplicative renormalisability for these renormalisation functions. As a last step we compare the two results coming from the solution of the Schwinger-Dyson equations and multiplicative renormalisability in order to derive the necessary constraints on the vertex function. These constitute the main results of this part of the thesis. In the weak coupling limit the solution of the Schwinger-Dyson equations must agree with perturbation theory. Consequently, we can find additional constraints on the 3- point vertex by perturbative calculation. Hence, the one loop vertex in QED is then calculated in arbitrary covariant gauges as an analytic function of its momenta. The vertex is decomposed into a longitudinal part, that is fully responsible for ensuring the Ward and Ward-Takahashi identities are satisfied, and a transverse part. The transverse part is decomposed into 8 independent components each being separately free of kinematic singularities in any covariant gauge in a basis that modifies that proposed by Ball and Chiu. Analytic expressions for all 11 components of the O(a) vertex are given explicitly in terms of elementary functions and one Spence function. These results greatly simplify in particular kinematic regimes. These are the new results of the second part of this thesis.

176 leaves : appendices / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Mathematical Physics, University of Adelaide, 1971

Thesis (Ph. D.)--Montana State University--Bozeman, 2007. / Typescript. Chairperson, Graduate Committee: William A. Hiscock. Includes bibliographical references (leaves 55-60).

Thesis (Ph.D.) -- Dept. of Mathematical Physics, University of Adelaide, 1971.

Thesis (Ph. D.)--Oregon State University, 2000. / Typescript (photocopy). Includes bibliographical references (leaves 74-76). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 163-169).

In recent years, a large number of black holes have been presented as candidates for an evasion of the "no-hair" conjecture. These examples typically have two features: a non-Abelian gauge field and instability. A large part of this thesis is devoted to a detailed study of the Einstein-Yang-Mills-Higgs (EYMH) black holes, including the analytic proof of the evasion of the "nohair" theorem in this case and proving that the black holes are unstable. We also consider an example of a "hairy" black hole not involving a non-Abelian gauge field, which arises in a higher derivative model of gravity derived from string theory, and prove analytically how the "no-hair" theorem is evaded. The rest of this thesis is concerned with the thermodynamics and quantum field theory of these black holes. In a first order approximation to the unknown theory of quantum gravity, we calculate the entropy of the "hairy" black holes. This turns out to be divergent, and parts of the divergences are attributed to the effect of hair on information loss processes occurring as the black hole evolves in time. We pursue this idea further by making a preliminary estimate of the magnitude of the quantum de-coherence effects on the state of the quantum field as time proceeds. These processes may be of interest phenomenologically in the future. The extension of the theory to non-static geometries is also discussed, by describing the results of bringing rotation into the picture. We prove that the Hartle-Hawking state is not regular everywhere outside the event horizon of a Kerr black hole, with the result that quantum field theory on rotating black hole space-times is more complicated than on static geometries.

Renormalisation is an important aspect of Quantum Field Theory. It is used to create physically meaningful theories and some major developments took place in the 1970's and onwards. We consider Renormalisation in its application to the theories of ψ⁴ , Quantum Electrodynamics, Quantum Chromodynamics and the Background Field Method. Feynman diagrams are used to illustrate many of the concepts.