Break up processes involving a three body system in the Coulomb field are studied. A method is developed for the realistic treatment of such a system, and is applied to the break up of the nucleus, ⁷Li. The Simple Cluster Model of ⁷Li and the Coulomb excitation code COULVAR are used for the calculations. The continuum states of the α + t system are treated as a set of discrete states, by confining the relative motion of the clusters to a spherical box. The infinite set of states is then truncated by imposing an energy cutoff so that only the states below this energy are considered. The density of these states varies according to the box radius and the energy cutoff. The stability of the model is tested by varying these two parameters. The corresponding calculated probability of excitation of ⁷Li has converged for a box radius of 20 fm and an energy cutoff of 20 MeV. The level energies and the wavefunctions of the continuum states are then easily obtained and are used to calculate the important matrix elements for the electromagnetic transitions between the bound states and the continuum states of ⁷Li. The method is used to calculate the probability of excitation of ⁷Li to its first excited state in the inelastic scattering experiments. It successfully reproduces a range of available data. An approximation is then developed to calculate the nuclear-Coulomb interference at low energies (well below the Coulomb barrier). The results of its application supports the need for renormalisation of the nuclear potentials suggested by inverse scattering calculations. The method closely reproduces The ⁷Li data in this region with the refitted nuclear potentials. The application of the three body model to the break up of ⁷Li on heavy targets at high energies produces very interesting results. It predicts reasonably good cross sections in the regions of pure Coulomb interaction. It also shows that at high energies the nuclear forces become very strong and affect the classical Rutherford orbit of the projectile. These effects are enhanced for heavier targets and the observed small scattering angle should not be taken as the angle of a classical orbit. Finally improvements towards the generalisation of the method are suggested so that it will be capable of coping with any three body system in a strong Coulomb field.

This work is principally concerned with the operator approach to the orbifold compactification of the bosonic string. Of particular importance to operator formalism is the con formal structure and the operator product expansion. These are introduced and discussed in detail. The Frenkel-Kac-Segal mechanism is then examined and is shown to be a consequence of the duality of dimension one operators of an analytic bosonic string compactified on a certain torus. Possible generalizations to higher dimension operators are discussed, this includes the cross-bracket algebra which plays a central role in the vertex operator representation of Griess's algebra, and hence the Fischer-Griess Monster Group. The mechanism of compactification is then extended to orbifolds. The exposition includes a detailed account of the twisted sectors, especially of the zero-modes and the twisted operator cocycles. The conformal structure, vertex operators and correlation functions for twisted strings are then introduced. This leads to a discussion of the vertex operators which represent the emission of untwisted states. It is shown how these operators generate Kac-Moody algebras in the twisted sectors. The vertex operators which insert twisted states are then constructed, and their role as intertwining operators is explained. Of particular importance in this discussion is the role of the operator cocycles, which are seen to be crucial for the correct working of the twisted string emission vertices. The previously established formalism is then applied in detail to the reflection twist. This includes an explicit representation of the twisted operator cocycles by elements of an appropriate Clifford algebra and the elucidation of the operator algebra of the twisted emission vertices, for the ground and first excited states in the twisted sector. This motivates the 'enhancement mechanism', a generalization of the Frenkel-Kac-Segal mechanism, involving twisted string emission vertices, in dimensions 8, 16 and 24. associated with rank 8 Lie algebras, rank 16 Lie algebras and the cross-bracket algebra for the Leech lattice, respectively. Some of the relevant characters of the 'enhanced" modules are determined, and the connection of the cross-bracket algebra to the phenomenon of 'Monstrous Moonshine' and the Monster Group is explained. Algebra enhancement is then discussed from the greatly simplified shifted picture and extensions to higher order twists are considered. Finally, a comparison of this work with other recent research is given. In particular, the connection with the path integral formalism and the extension to general asymmetric orbifolds is discussed. The possibility of reformulating the moonshine module in a 'covaxiant' twenty-six dimensional setting is also considered.

We discuss the algebraic geometry of certain finite energy, static field configurations of an SU(N) Yang - Mills - Higgs theory in the limit of a massless scalar field and how it may be applied to their construction. We develop a systematic way of locating solutions with spherical or cylindrical symmetries. Consideration of the fields' regularity is extended from SU(2) to SU(3) as also is the description of the general monopole configuration.

Dimensional regularisation is formulated without using the assumption that f d(^D)k(k(^2))(^n) = 0. Alternative definitions of ϵ(_kλµv) and γ(^5) are also considered. In the reformulated scheme, quadratic divergences are present, in general, in the scalar and gauge boson self-energies, and remain unregularised. The possible cancellation of such divergences is investigated. Phenomenological aspects of unified gauge theories are studied.

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Singularities ~n General Relativity are due to incompleteness of space-time. This thesis examines the relationships between some of the different notions of incompleteness of a manifold with connection, together with the stability of geodesic completeness and incompleteness. Some p(parallelisation)-completions of Rand S1 are compared with the b(bundle)-completions, and the applicability of the p-boundary construction to General Relativity is discussed. Relationsips are shown between g(geodesic), b(bundle) and b.a.(bounded acceleration) incompleteness. Further acceleration is dependent notions of incompleteness are defined, and it shown that A they are all equivalent to the existing notions of completeness for a Riemannian manifold. The Whitney C K topologies provide a way of topologising the space of metrics on a manifold, in order to consider stability of geodesic completeness or incompleteness. It is shown how the spaces of connections and sprays may also be topologised, and the continuity of some important mappings is demonstrated. It turns out that for R both geodesic completeness and incompleteness are stable with respect to perturbation of the spray. Incompleteness of st ~s also stable, but the complete sprays are closed. For S1~S1 and R~S1 it is shown that null and time like geodesic completeness and incompleteness all fail to be stable with respect to the space of Lorentz metrics. Given a connection/spray on a pair of manifolds, one can construct a connection/spray on their product, and this is used to show how instability of completeness/incompleteness may arise if the product ~s compact. It is also shown how to induce sprays on the retraction of a manifold.

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The most important problems in the philosophy of quantum mechanics are the problem of measurement and the problem of the 'acausal' EPR correlations. It is commonly thought that these problems call for a new interpretation of the quantum theory. I argue that it is possible to construe both problems rather differently, as resulting from a mistaken understanding of scientific theory-application. It then becomes possible to tackle both problems independently of questions of interpretation, by attending carefully to what constitutes a successful application of a scientific theory, and of the quantum theory in particular. In the first part of the Thesis, I argue against a standard conception of scientific theory-application. This standard conception, which is often presupposed in the philosophical discussions of quantum mechanics, takes the applications of a scientific theory to constitute its domain of empirical adequacy. I argue that, on the contrary, a scientific theory can be applied to phenomena that it does not subsume. I present a case study in the history of superconductivity to illustrate and to motivate this claim. In the second part, I argue that the problem of measurement can be construed as the impossibility of applying the quantum theory to measurement interactions. I then argue that Arthur Fine's proposed solution to the measurement problem implicitly abandons the standard conception of application. Finally I look at quantum correlation phenomena. Bas Van Fraassen has claimed that the EPR correlations fit no causal model. The correctness of this claim depends on what probabilistic constraints a causal model is taken to have to satisfy. I argue, following Nancy Cartwright, that Van Fraassen's constraints on common-cause models are too strong; and I describe a direct-cause model that, I urge, constitutes a successful application of the quantum theory to the EPR correlations.