The goal of this thesis is to investigate the relation between mathematics and physics and the role this relation plays in what physics does best, that is in scientific explanations. The case of gauge theories, which are highly mathematical, is used as an extended case study of how mathematics relates to physics and to the world and these relations are examined from both a historical and a philosophical perspective. Gauge theories originated from an idea of Weyl which turned out to be wrong, or in other words, empirically inadequate. That original idea underwent a dramatic metamorphosis that turned the awkward caterpillar into a beautiful butterfly called gauge theories, which were very successful and dominated theoretical physics during the second half of the twentieth century. The only leftover from Weyl's faux pas was the very name of the theories and the question how it is possible for something as wrong as his original idea to result in a theory so relevant to the world. We argue that it is thanks to a very dynamic and dialectic relation between mathematicians and physicists, both theoretical and experimental, that the resulting theory turned out to be so successful. From a more philosophical perspective, we take the view that the relation between mathematics and physics has a structuralist character, in general, and we recognize that what we call ambiguity of representation of the third type lies at the heart of gauge theories. Our claim is that it is precisely this type of ambiguity of representation and the non-physical entities that it inevitably introduces which ex-plain the physical facts. However, the non-physical entities should be attributed a non-causal status in order to provide valid and legitimate scientific explanations. The fibre bundles formulation of gauge theories is considered to be their unique formulation that allows for this shift and the Aharonov-Bohm effect which is examined within the fibre bundle context provides a narrower yet very fruitful case study.

We analyse the most general N = 2 supersymmetric solutions of d = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a sevendimensional Riemannian manifold Y7. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y7. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ordinary differential equation. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS4×S7 solution with non-trivial four-form flux. Furthermore, we study supersymmetric asymptotically locally AdS4 solutions of N = 2 gauged supergravity which via the AdS4/CFT3 correspondence are dual to supersymmetric gauge theories on deformed 3-spheres with SU(2)×U(1) symmetry and a non-trivial background gauge field. These solutions lift to solutions of M-theory and we show that the gravitational free energy agrees with the large N limit of the dual field theory free energy, obtained from the localized partition function of a class of N = 2 Chern-Simons-matter theories. In this context, we present a complete class of supersymmetric backgrounds of N = 2 gauged supergravity whose conformal boundary is a biaxially squashed Lens space S3/Zp. Generically we find that the latter admits Taub-NUT-AdS fillings, with topology R4/Zp, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology.

The type IIA and type IIB supergravity actions in d = 10 dimensions are the low-energy effective theories of type IIA and IIB string theory. In addition, the unique eleven dimensional supergravity theory is the low-energy effective action of M-theory. Higher order corrections to the low-energy effective actions of these supergravity theories contain perturbative and non-perturbative effects of the corresponding string theories and, as such, understanding the structure of the higher order terms provides an insight into the perturbative and non-perturbative formulations of string theory. The U-duality groups of type IIA/B string theory and M-theory compactified on a torus to d < 10 dimensions puts powerful constraints on the higher derivative terms in the effective actions of these theories. In particular, the higher derivative terms in d = 10 - n dimensions are required to possess coefficient functions that transform as En+1 (Z) automorphic forms. These automorphic forms are complex mathematical objects that encode all the perturbative and non-perturbative features of type II string theory and M-theory compactified on an torus to d dimensions. We investigate the structure of the higher derivative terms and their associated automorphic forms in the effective actions of type IIA/B string theory and M-theory. Constraints on automorphic forms appearing in d dimensions by dimensional reduction of arbitrary higher derivative terms in the type IIA, type IIB and M-theory effective actions to d dimensions are obtained. The behaviour of higher derivative terms in the d dimensional type II effective action in specic limits of various parameters is analysed. We derive a group theoretical interpretation for each limit. A general formula is given for a class of automorphic forms in these limits.

The infinite-dimensional symmetry algebra of a conformal field theory (CFT), the Virasoro algebra, is generated by the holomorphic and anti-holomorphic part of the stress tensor. Besides such 'chiral symmetries' the CFT also has an integrable symmetry, that is, infinite families of commuting conserved charges. In this thesis a step towards combining these two symmetries into a single formalism is taken, by identifying integrable stuctures of a CFT through studying the representation category of the underlying chiral algebra. Then by introducing defects in the system, conserved charges can be constructed by perturbing certain conformal defects. Starting from an abelian rigid braided monoidal category C one defines an abelian rigid monoidal category C_F which captures some aspects of perturbed conformal defects in two-dimensional CFT. Namely, for V a rational vertex operator algebra one considers the charge-conjugation CFT constructed from V (the Cardy case). Then C = <strong>Rep</strong>(V) and an object in C_F corresponds to a conformal defect condition together with a direction of perturbation. To each object in C_F one assigns a perturbed defect operator on the space of states of the CFT and then shows that the assignment factors through the Grothendieck ring of C_F. This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.

A study was made of Monte Carlo simulations of the channel pp -> ḡḡ -> bbμ+μ+(or b¯b¯μ¯μ¯) + jets + missing ET which offers a realistic possibility of searching for supersymmetry. This has a distinctive signature of two same-sign muons in half of the events. After reconstruction, requirements were imposed on the PT, isolation and impact parameter of the muons. Events were also required to have either four jets with ET greater than a threshold that was varied or missing ET greater than a variable threshold. With these requirements, the backgrounds were reduced to a level equal to or less than that of the signal. If four jets with ET > 35 GeV were required, the signal-to-background ratio was 1.2 ± 0.3 (statistical)+0.6/-0.4(systematic) +0.8/-0.5(theoretical) when low luminosity pile-up was added to the signal. The minimum integrated luminosity required to obtain a 50" excess of signal events was estimated to be [5.6 +1.4 (statistical) +2.3 (systematic) +1.9 (theoretical)] fb-1. A larger signal-to-background ratio of 2.3 ± 0.5 (statistical)+0.6/-0.3(systematic) +1.5/-1.1(theoretical) could be obtained by increasing the jet ET threshold to 50 GeV. Testbeam data were analysed on lead tungstate crystals and vacuum phototriodes for the CMS electromagnetic calorimeter endcaps. A potential instability of the vacuum phototriodes was found, which is believed to be due to movement of caesium within the electrode coatings; this was reduced by illumination with a 100 Hz laser. The energy resolution for electron reconstruction in a 3x3 matrix of endcap crystals was (1.21 ± 0.05)% at 120 GeV, which was worse than expected. This was partly due to additional noise from barrel-type VFE cards. Position resolution using the log weighting method applied to the same 3x3 matrix was (0.96 ± 0.02) mm. Formation of colour centres was investigated by repeatedly irradiating the crystals with 120 GeV electrons, alternating with injection of a 440 nm monitoring laser. For six crystals, the exponents a of power law fits to electron and laser amplitudes had a mean of 1.15 and a standard deviation of 0.06. The intercalibration error due to absorption of scintillation light by colour centres was restricted to 0.2% provided that the correct value of a for a crystal or its mean value for a set of crystals was used

Part 1. examines the reversibility in time of quantised fields. It is shown that reversibility of a certain kind (that of Schwinger) is a concomitant of Lorentz invariance, rather than an independent symmetry to be imposed on the theory. Part 2. is an account, with some new applications, of work of T.R.R. Skyrme. First we derive his closed forms for propagators from canonical quantum theory, rather than from the Feynman quantization of classical fields. The discussion is then specialised to the one nucleon propagator and a variational method developed. With a very simple form of trial function this is applied to the ,no-recoil neutral scalar theory, where it is shown to give accurately that part of the propagator which describes the real nucleon. A similar approximation is then used in the pseudoscalar symmetric no-recoil theory, and found to give correctly the electrical properties of the nucleon in the weak and strong coupling limits. Finally a closely related trial function is used in the relativistic symmetric (P.S.,P.S.) theory, where we extend Skyrme's work on the nucleon anomalous magnetic moments to obtain also the socalled "neutron-electron interaction".

Electromagnetic imaging currently plays a vital role in various disciplines, from engineering to medical applications and is based upon the characteristics of electromagnetic fields and their interaction with the properties of materials. The detection and characterisation of metallic objects which pose a threat to safety is of great interest in relation to public and homeland security worldwide. Inspections are conducted under the prerequisite that is divested of all metallic objects. These inspection conditions are problematic in terms of the disruption of the movement of people and produce a soft target for terrorist attack. Thus, there is a need for a new generation of detection systems and information technologies which can provide an enhanced characterisation and discrimination capabilities. This thesis proposes an automatic metallic object detection and classification system. Two related topics have been addressed: to design and implement a new metallic object detection system; and to develop an appropriate signal processing algorithm to classify the targeted signatures. The new detection system uses an array of sensors in conjunction with pulsed excitation. The contributions of this research can be summarised as follows: (1) investigating the possibility of using magneto-resistance sensors for metallic object detection; (2) evaluating the proposed system by generating a database consisting of 12 real handguns with more than 20 objects used in daily life; (3) extracted features from the system outcomes using four feature categories referring to the objects’ shape, material composition, time-frequency signal analysis and transient pulse response; and (4) applying two classification methods to classify the objects into threats and non-threats, giving a successful classification rate of more than 92% using the feature combination and classification framework of the new system. The study concludes that novel magnetic field imaging system and their signal outputs can be used to detect, identify and classify metallic objects. In comparison with conventional induction-based walk-through metal detectors, the magneto-resistance sensor array-based system shows great potential for object identification and discrimination. This novel system design and signal processing achievement may be able to produce significant improvements in automatic threat object detection and classification applications.

No description available.

The present thesis contains the development of new techniques to compute the Yukawa couplings for the fundamental matter in the context of string theoretic Brane World Models. Exploiting the' unitarity of String Theory these couplings are derived by means of factorisation of the classical limit of the two-loop twisted partition function in generic toroidal compactifications. In fact by taking the Schwinger time of the strings propagating in the loops to infinity, the string theoretic diagram is reduced to a field theoretic interaction involving the low-lying states of oscillations of the so-called twisted strings. These are strings stretched between two D-Branes either intersecting at angles or with different magnetic fields turned on in their world-volumes and they reproduce four dimensional chiral fermions in the low energy limit of the theory. The models involving intersecting or magnetised D-Branes are related to one another by means ofT-Duality. The factorisat~on of the resulting diagram yields three propagators and two complex conjugate copies of the sought Yukawa couplings, whose moduli dependence (both on the open and on the closed string moduli) is determined in full generality in toroidal compactifications of the models. The actual partition function is computed, by using the conformal properties of String Theory, in the closed string channel, in which it becomes a tree-level interaction between three closed strings ending on magnetised D-Branes. The computation performed is generalised to the case of g+l external states and it corresponds to the g-loop twisted partition function in the open string channel. The fundamental ingredients for the calculation are the Reggeon vertex for the emission of g+ 1 off-shell closed strings and the boundary state fOf a wrapped magnetised D-Brane. A careful analysis of the phase factors involved in determining the form of these objects in toroidal compactifications leads also to a generalisation of the known T -Duality rules.

No description available.