As investigation into the nature of elementary particles reachs ever greater energies, more and more hadrons of high-spin are produced. A few of the many problems attending the theoretical description of such particles are tackled here. In chapter 2 the basic formalism and notation used throughout is introduced. Chapters 3 and 4 deal -/ith the functions arising from high-spin wave functions and projection operators. The problem of parametrising the vertex function (three-point function) coupling three on-mass shell particles in the most general form consistent with Lorentz invariance is dealt with in chapter 5. The 'helicity' and the 'covariant' schemes of parametrisation are outlined. Using the 'covariant' formalism,the feasiblity of the narrow widths of recently reported high-spin meson resonances is discussed in chapter 6. In chapter 7 single-particle exchange processes involving high-spin hadrons are considered. Differential cross sections and helicity density matrices are calculated for several specific cases. The results for spin-1 exchange are applied to the problem of the electroproduction of high spin hadrons in chapter 8.

The first part of the thesis deals with the relations among meson-baryon scattering amplitudes detained under various collinear symmetries. The auxiliary group and its role in constructing relativistic field theories that incorporate internal symmetries is developed in the introductory chapter following Feldmann and Matthews. The collinear groups, in particular S(U(3)U(3)) is discussed in detail. Various predictions among the mesonbaryon scattering amplitudes are worked out under this group and also under SU(6)w and compared with experimental data. These processes are also considered under the collinear groups SU(4)w and S(U(2)U(2))I.Y. These smaller groups are used to compare the effects of symmetry-breaking in SU(3) and SU(4). The second part examines the decomposition of the unitary irreducible representations of SL(2,c) restricted to U(1)^T(2) and SU(l,l). Integral representations for unitary matrices that allow to pass from one set of basis vectors to another (labelled by the corresponding Casimir operators of the subgroups SU(2), SU(1,1) and U(1)^T(2)) are derived using the theory of Induced Representation.

The time variations of Cosmic Ray intensity have been studied by means of two sets of directional meson telescopes situated at I) London, U.K., a medium latitude station (51°.32° N) and 2) Kampala, Uganda, a low latitude station (0.33 N). At London two telescopes inclined at 45° to the zenith were made to point in the North and the South directions. At Kampala, two similarly inclined telescopes were directed in the East and West directions. The main purpose of using directional telescopes at the two locations was to separate out that part of the daily variation which is due to a primary anisotropy from that induced by atmospheric temperature effects, as the latter cannot be determined by direct methods. Data from the North/South telescopes have been used to study the atmospheric effects on the particles recorded. Pressure and Temperature coefficients have been obtained by regression analysis between the atmospheric variables and the Cosmic Ray intensity. The different procedures normally employed for correcting meson data are compared and critically examined. The London (North/South) data have also been used to study the characteristics of the solar anisotropy during the ascending phase of the present solar cycle. (After correction for atmospheric effects). The analysis revealed that the solar diurnal vectors had increased in going from 1965 to 1967, for both the North and South telescopes. A comparison of the observed diurnal vectors with the predictions of a free-space anisotropy of amplitude 0.4% and phase 1800 hrs. L.S.T., (as suggested to be obtaining in recent years by extensive neutron-monitor measurements), reveals that the observed changes in the diurnal waves over 1965-67 may be attributed to an increase in the upper limiting rigidity of co-rotation from about 40 Gv during 1965 to 80 Gv in 1967. An extensive analysis has also been carried out to investigate the correlation on a day to day basis between the diurnal and semi-diurnal vectors as observed by the N/S telescopes with those observed by a high latitude neutron monitor. The correlation of the diurnal vectors with the level of geomagnetic activity has also been investigated. Data obtained from the Makerere, Kampala telescopes over the period July 1964-Apr. 67 have also been analysed for the solar daily variation. It was observed that during the years-1964-65 the solar diurnal variations in the pressure corrected data, from both the recorders at Makerere, had an amplitude of 0.2% and a time of maximum at about 14.30 hrs. L.S.T. The absence of any appreciable phase difference between the E/W recorders at Makerere also suggests that there was no appreciable primary anisotropy in the medium range of energies, (50-150 Gv) at the minimum of the solar cycle No. 19. A gradually increasing phase difference observed over 1964-67 suggests a return of the diurnal anisotropy as the solar activity builds up. (It is found that a major part of the diurnal and semi-diurnal variations observed during this period can be attributed to instrumental temperature effects). The results on the S.D.V. obtained by the London recorders have been compared with those obtained at Manchester over the period 1948-54 (i.e. the declining phase of the solar cycle No. 18). It is found that the phase of the diurnal vectors observed during 1949-52 was significantly earlier that that measured more recently in London. Further- more the azimuthal streaming of the cosmic rays in the solar system due to the co-rotation of the cosmic rays gives a time of maximum of 18.00 hr. to the diurnal variation at the earth, The Manchester data for the above period cannot be reconciled with the co-rotation theory. In fact it is necessary to postulate the presence of an anisotropy with an earlier tine of maximum than 18.00 hr. to explain the Manchester data and it appears that this component may be present during certain portions of the solar cycle. Data acquired from the Carnegie Institution stations (Ionization Chambers), over the period 1937-66 has been studied in conjunction with the predictions of the co-rotation theory. There appears to be a systematic difference between these data and the predictions of the theory. As in the case of the Manchester recorders, a vector with a time of maximum earlier than 18.00 hrs. is required to explain the results during some parts of the solar cycle. Apart from this discrepancy, bosh the Manchester data and the Carnegie Institution data indicate a reduction in upper limiting rigidity during years of the minimum of the solar cycle. The onset recovery characteristics and the rigidity dependence of several Forbush decreases occurring during 1966-67 have been studied. For these investigations data from high counting rate neutron monitors have been used along with data acquired from the N/S recorders at London and the E/W recorders at Makerere. The results have been compared with those of earlier investigations and the areas of agreement and disagreement explored.

This thesis describes the dynamics of particles in periodic potentials with a constant acceleration force and a tilted harmonic trap. The particles exhibit non-KAM chaos, whose semi classical trajectories are a combination of Bloch and harmonic oscillations. When the frequencies of these two oscillations are commensurate, the phase space is threaded by a stochastic web, along which the particles can diffuse rapidly. vVe find that the stochastic web rings, whose radii correspond to the roots of Bessel functions , found in the semiclassical analysis confine the electron to a finite region in real space, both in a semiclassical and a full quantum picture. Firstly, we study electron transport in a semiconductor supedattice when an electric field and a tilted magnetic field are applied. The tiltcd magnetic field spatially offsets the Landau-like eigenstates, induced by the magnetic field , and tunnel coupling is allowed. The overlap integral of quantized electron states in ad.i-acent quantum wells, which determines the tunnel coupling and the extent of the quantum wavefunctions, vanishes at the zeros of the Bessel functions , precisely the same position where, semi classically, the electron is trapped by the rings of the stochastic web, suggesting remarkable synergy between the semi classical and quantum regimes. Secondly, we consider neutral 23Na atoms falling under the influence of gravity through a periodic lattice potential, created by the interference pattern of two counter-propagating laser beams. A harmonic trap is applied tilted to the lattice axis. The atom trajectories undergo dramatic abrupt extension in the vertical direction and map out intricate web patterns in momentum phase space when the Bloch frequency and a frequency corresponding to the harmonic trap arc commensurate. We find three indicators of a resonant trajectory, which are the maximal vertical displacement, the longest return time to the origin, and the sign change of a momentum component. Since the Bloch frequency is determined by the gravitational acceleration, g, and the appearance of the chaotic resonance point is very sensitive to the Bloch oscillation frequency, the onset of chaos can measure g with a small relative uncertainty 6.g/ 9 = 4 X 10 - 7 . We also investigate the dynamics of a quantum wavepacket ill the system, using the Crank-Nicolson method to solve the time-dependent Schrodinger equation with our fast GPU tridiagonal matrix solver. Estimating the quantum mean trajectory and the wavepacket evolution, the

The exploration of several supersymmetric parameter spaces implementing experimental constraints including those from both collider and dark matter relic density considerations and using a Bayesian approach is undertaken. Two scanning methods were used in conjunction with this, both the more customary l\Iarkov-Chain Monte Carlo (MGMC) technique, and also the recently developed Nested Sampling method. Using the power and utility of such formalism, a first Bayesian investigation of the Non Universal Higgs Model (NUH~d) was made, as well as a first full scan of the Constrained Next-to-l\1inimal Supersymmetric Standard Model (CNrvISSM). In addition this technique was also applied to the 'ideal Higgs scenario' in the NMSSM in order to efficiently find points of interest. As well as producing probabilistic interpretations of the parameter spaces in question, the Nested Sampling approach allows some qualitative model comparison to be made between the models studied, to see which best fit the data. In addition, some general practical lessons about the sensible interpretation of a Bayesian scan are presented and commented on, and the issue of generation of heavy higgsino dark matter (a common feature in all the models studied) via the RGEs is also addressed, with a specific focus on a novel mild focusing effect in the NUHM.

This thesis presents en account of the analysis of the reactions π(^+) D → P(_s) P wº and π(^+) D → P(_s) P ηº at 4.0 GeV/c incident momentum, carried out by the author whilst at the University of Durham. The experiment, undertaken in collaboration with the University of Birmingham and the Rutherford Laboratory, is described in detail, particular emphasis being applied to the limitations of the experimental setup, the accuracy of the resulting data and the problems associated with the use of a deuterium target. Following a description of the selection of the channel π(^+) → P(_s) P π (^+) π(^-) π(^o) the production and decay processes of the w(^o) - mesons are analysed in detail. The results are compared with those from previous analyses and with the predictions of various Regge Pole models. To describe the various features of the data it is found necessary to infer the presence of significant contributions from unnatural parity exchanges such as the B - meson, in disagreement with the earlier theoretical interpretations which assumed the complete domination of the natural parity component, namely p - exchange. As part of this analysis the nature of the associated background is determined, and the results indicate the possible breakthrough of events from the 4c channel, π(^+)D → P(_s) P π(^+) π(^-)The characteristics of these events in the 1.0 GeV/c(^2) region of the tripion mass spectrum is investigated, and it is concluded that they may well affect the interpretation of the observed enhancements attributed to the controversial H and A(_1) resonances. Finally the production mechanism of the η - meson is analysed.

We explore various interactions in D-brane configurations and their implications for the construction of phenomenologically viable string models. Initially, we investigate the scenario of parallel and perpendicular stacks of D-branes located on an orbifold singularity, as in the bottom-up construction. A supersymmetric D-brane model is presented, that has CP spontaneously broken by discrete torsion. The low energy physics is largely independent of the compactification scheme and the kahler metric has 'texture zeros’ dictated by the choice of discrete torsion. This motivates a simple ansatz for the kahler metric which results in a CKM matrix given in terms of two free parameters, hence we predict a single mixing angle and the CKM phase. The CKM phase is predicted to be close to /3.We then proceed to a discussion of a different class of models involving D-branes intersecting at arbitrary angles, and wrapping a compact internal space. Here we calculate tree level three and four point scattering amplitudes in type II string models with matter fields localised at D-brane intersections. We treat both the classical and quantum parts in detail, with the latter being computed using conformal field theory techniques developed for closed strings on orbifolds. Contributions from string states wrapping the internal space are also included. These calculations are then generalised to TV-point amplitudes, which are determined completely. Finally, we consider the application of these results to four fermion interactions. In particular, the implications for Higgs exchange in intersecting brane models is discussed.

Soft and collinear singularities, known collectively as infrared singularities here, plague the calculation of scattering amplitudes in gauge theories with massless particles such as QCD. The aim of this thesis is to describe methods of deriving amplitudes that are infrared finite and therefore do not suffer from this problem. We begin with an overview of scattering theory which includes a detailed discussion of the source of infrared singularities and outlines approaches that can be used to avoid them. Taking one of these approaches, namely that of dressed states, we give a detailed description of how such states can be constructed. We then proceed to give an explicit example calculation of the total cross section of the process e+e(^-) →2 jets at NLO. In this example we construct dressed amplitudes and demonstrate their lack of infrared singularities and then go on to show that the total cross section is the same as that calculated using standard field theory techniques. We then move on and attempt to improve the efficiency of calculations using dressed states amplitudes. We describe some of the problems of the method, specifically the large numbers of diagrams produced and the multiple different delta functions present in each amplitude. In attempting to fix these issues we demonstrate the difficulties of producing covariant amplitudes from this formalism. Finally we propose the use of the asymptotic interaction representation as a solution to these difficulties and outline a method of producing covariant infrared finite scattering amplitudes using this.

A mathematical description of the electromagnetic fields of non-paraxial laser beams is derived and used to calculate the trapping forces on spherical particles. The fields are exact solutions to the wave equation. A set of closed-form expressions for the scalar field of such a beam is presented first. The solution for the order 00 is equivalent to the wave of a combined complex-point source and sink. In the far field the two lowest order solutions, 00 and 01, closely match the energy density produced by a high-numerical aperture lens illuminated by a paraxial Gaussian beam. At the large beam waist limit these two solutions reduce to the paraxial beam form. However, it is found that only the 01 order solution is physically realizable, since the total energy flux through the transverse section of the 00 order beam is infinite. The scalar solutions of arbitrary order are then used to derive solutions to the vector wave equation. Next, the electric and magnetic fields that closely fit the far-field boundary conditions for a focusing lens are constructed from the solutions for the orders 00 and 01. These fields are in general elliptically polarized at the beam waist. However at the large beam waist (paraxial) limit and in the far field limit the fields become linearly polarized. The electromagnetic field due to order 01 is used to calculate the Maxwell stress tensor, and hence the trapping forces exerted on a dielectric microsphere in a single beam laser tweezers setup. It is demonstrated that the electromagnetic theory model based on the 5th order Gaussian beam approximation due to Barton is accurate for almost paraxial beams (numerical aperture NA<0.25), when compared to the model derived here. However, for strongly focused beams (NA>l) the 5th order approximation breaks down. Trapping forces on water droplets suspended in air and on polystyrene spheres suspended in water, exerted by a Gaussian laser beam focused with lenses of various numerical apertures are calculated. It is established that a model accurate for a strongly focused beam is vital, since in order to trap a particle effectively a focusing lens with NA>1 is required.

A search for particles carrying an electric charge one third that of the electronic charge (quarks) has been carried out close to the core of extensive air showers. The search was conducted at sea-level using a large volume flash tube chamber. The technique employed utilised these nativity of flash tubes to particle ionisation. Air showers were selected by requiring the local electron density above the detector to exceed 40 m (^-40) with this trigger the apparatus has been operated for 2570 hours. No definite quark tracks have been observed, the upper limit on the quark flux being set at 8.0 x 10 (^-11) cm (^-2) sec (^-1) st (^-1). In the same experiment, the energy spectra of charged and neutral nuclear-active particles in extensive air showers of mean shower size 2.0 x `0 (^5) has been measured. A method has been developed for estimating the energies of the particles from the width of the nuclear-electromagnetic cascade resulting from the interactions, as measured in flash tubes below the absorbers. The results have been related to extensive air shower characteristics; in particular to the nuclear-physical aspects of very high energy collisions. The flash tube chamber has been modified to allow the relationship between the width of the nuclear-electromagnetic cascade and the energy of the interacting particle to be established. The experiment, utilising the flux of unaccompanied hadrons in the near-vertical direction, has also allowed the energy spectrum of these particles to be determined up to energies of ITeV.