Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Ion bombardment induced compositional changes in compound semiconductor surfaces studied by XPS combined with LEISS

Surface compositional change of GaP, GaAs, GaSb, InP, InAs, InSb, GeSi and CdSe single crystals due to low keV noble gas ion beam bombardment has been investigated by combining X-ray Photoelectron Spectroscopy (XPS) and Low Energy Ion Scattering Spectroscopy (LEISS). The purpose of using this complementary analytical method is to obtain more complete experimental evidence of ion beam modification in surfaces of compound semiconductors and GeSi alloy to improve the understanding of the mechanisms responsible for these effects. Before ion bombardment the sample surfaces were analysed nondestructively by Angular Resolved XPS (ARXPS) and LEISS to get the initial distribution of surface composition. Ion bombardment experiments were carried out using 3keV argon ions with beam current of 1μA for a period of 50 minutes, compositional changes in the surfaces of compound semiconductors and GeSi alloy were monitored with normal XPS. After ion bombardment the surfaces were re-examined with ARXPS and LEISS. Both XPS and LEISS results showed clearly that ion bombardment will change the compositional distribution in the compound semiconductor and GeSi surfaces. In order to explain the observed experimental results, two major theories in this field, Sigmund linear collision cascade theory and the thermodynamic models based on bombardment induced Gibbsian surface segregation and diffusion, were investigated. Computer simulation using TRIM code was also carried out for assistance to the theoretical analysis. Combined the results obtained from XPS and LEISS analyses, ion bombardment induced compositional changes in compound semiconductor and GeSi surfaces are explained in terms of the bombardment induced Gibbsian surface segregation and diffusion.