In this work we have undertaken the study of some aspects of higher spin relativistic wave equations of the first order. These aspects are their definiteness of charge, their second quantization and their causal propagation. The work is divided into three parts. In part one we have studied the Bhabha equations based on the sixteen and twenty dimensional representations and showed that the charge associated with them is indefinite. In part two we have studied in detail the Gel'fand Yaglom equations and showed that certain equations can have definite charge. Finally in part three we have studied the propagation in the external electromagnetic field of certain higher spin relativistic wave equations.

Typewritten Includes bibliographical references.

Thesis (P.H.D.)--University of Adelaide, Dept. of Physics, 1957. / Typewritten. Includes bibliographical references.

In this thesis we study relativistic models of gravitating uids with heat ow and electric charge. Firstly, we derive the model of a charged shear-free spherically symmetric cosmological model with heat ow. The solution of the Einstein-Maxwell equations of the system is governed by the pressure isotropy condition. This condition is a highly nonlinear partial di erential equation. We analyse this master equation using Lie's group theoretic approach. The Lie symmetry generators that leave the equation invariant are found. We provide exact solutions to the gravitational potentials using the rst symmetry admitted by the equation. Our new exact solutions contain the earlier results of Msomi et al (2011) without charge. Using the second symmetry we are able to reduce the order of the master equation to a rst order highly nonlinear di erential equation. Secondly, we study a shear-free spherically symmetric cosmological model with heat ow in higher dimensions. We establish the Einstein eld equations and nd the governing pressure isotropy condition. We use an algorithm due to Deng (1989) to provide several new classes of solutions to the model. The four-dimensional case is contained in our general result. Solutions due to Bergmann (1981), Maiti (1982), Modak (1984) and Sanyal and Ray (1984) for the four-dimensional case are regained. We also establish a new class of solutions that contains the results of Deng (1989) from four dimensions. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.

Nesse trabalho discutimos alguns aspectos da teoria quântica de campos que nos levam a formulação do potencial efetivo em teorias supersimétricas. O enfoque é dado as técnicas para análise da quebra de supersimetria em 2 + 1-dimensões. São discutidas as condições sobre o potencial efetivo de teorias supersimetrias para que ocorra ou não quebra de supersimetria. O potencial efetivo do modelo Wess-Zumino em 2+1-dimensões é calculado até a aproximação de 2-laços no formalismo de componentes e supercampos e até essa ordem não foi encontrado quebra de supersimetria. / In this work we discuss some aspects of quantum theory of fields used for the formulation of the effective potential of supersymmetric theories. The main focus is given to the methods used to analyse supersimmetry breaking in 2 + 1-dimensions. We discuss the conditions on the effective potential of supersymmetric theories for the occurrence of supersymmetry breaking. The effective potential of Wess-Zumino model em 2 + 1-dimensions is calculated up to 2-loops approximation where supersymmetry breaking is not found to this order.

Nesse trabalho discutimos alguns aspectos da teoria quântica de campos que nos levam a formulação do potencial efetivo em teorias supersimétricas. O enfoque é dado as técnicas para análise da quebra de supersimetria em 2 + 1-dimensões. São discutidas as condições sobre o potencial efetivo de teorias supersimetrias para que ocorra ou não quebra de supersimetria. O potencial efetivo do modelo Wess-Zumino em 2+1-dimensões é calculado até a aproximação de 2-laços no formalismo de componentes e supercampos e até essa ordem não foi encontrado quebra de supersimetria. / In this work we discuss some aspects of quantum theory of fields used for the formulation of the effective potential of supersymmetric theories. The main focus is given to the methods used to analyse supersimmetry breaking in 2 + 1-dimensions. We discuss the conditions on the effective potential of supersymmetric theories for the occurrence of supersymmetry breaking. The effective potential of Wess-Zumino model em 2 + 1-dimensions is calculated up to 2-loops approximation where supersymmetry breaking is not found to this order.

The subject matter of this thesis falls into two distinct parts. Chapters II to IV are devoted to a discussion of Schwinger's action principle, and chapters V and VI are concerned with the proof of dispersion relations for inelastic meson-nucleon scattering. The material of chapter II is based on some work done in collaboration with Dr. J.C. Polkinghorne, which has been published (Kibble and Polkinghorne 1957). This work was concerned with the clarification of certain points connected with the class of permissible variations in Schwinger's principle. There are, however, substantial changes in the present treatment, principally deriving from the introduction, in section II-5, of the concept of relative phases. This chapter is restricted to the case of non-relativistic quantum theory, and the discussion is extended to relativistic quantum field theory in chapter III. These chapters are devoted to a reformulation of Schwinger's action principle, and an investigation of the consequences of the new form of the action principle. Some of this material is necessarily contained in the work of Schwinger (1951, 1953a), but the treatment differs from his in several important respects. These are discussed in greater detail in section 2. Chapter IV is devoted to a discussion of higher order spinor Lagrangians, with particular reference to the use of a two-component field satisfying a second-order equation rather than a four-component spinor satisfying a first-order equation. This procedure has been suggested by Feynman and Gell-Mann (1958) in connection with their universal Fermi interaction. The work presented in this chapter was done jointly with Dr. J.C. Polkinghorne, and has been published (Kibble and Polkinghorne 1958). Chapters V and VI are devoted to a proof of the dispersion relations for the process in which a single meson is scattered on a nucleon into a state with several mesons. The proof follows the general lines of that by Bogolyubov, Medvedev and Polivanov (1956) for the case of elastic meson-nucleon scattering, This work has also been published (Kibble 1958). The notation employed in the thesis is summarized in appendix A. Appendix B is devoted to a discussion of consistency conditions on the Lagrangian function. The chapter number is omitted in references to sections or equations, except in the case of cross references between chapters.

Através do formalismo de supercampos, estudamos as propriedades ultravioletas da eletrodinâmica quântica supersimétrica no espaço-tempo tridimensional. Mostramos que esta teoria é finita em todas as ordens de perturbação num calibre particular. Também apresentamos uma análise perturbativa do modelo de Chern-Simons supersimétrico acoplado a um supercampo escalar complexo. Com isso, estudamos a quebra da simetria de calibre U(1) e calculamos as primeiras correções quânticas à ação efetiva na fase quebrada. Mostramos que a renormalização da equação de gap é suficiente para assegurar a renormalizabilidade do modelo em um laço de aproximação. Nós também verificamos que quando acoplado a um supercampo escalar sem massa, o modelo de Chern-Simons supersimétrico apresenta geração dinâmica de massa, um mecanismo que em D = 2 + 1 dimensões do espaço-tempo, diferentemente do modelo não-supersimétrico quadridimensional (Coleman- Weinberg), só ocorre a partir da aproximação de dois laços. Alguns outros resultados relacionados são também incluídos nesta tese, tais como um estudo do modelo CP**(N-1) não-comutativo supersimétrico e a equivalência entre os modelos de Maxwell-Chern-Simons e Auto-Dual supersimétricos. Em todo nosso trabalho, supersimetria é manifesta. / Within the superfield formalism, we study the ultraviolet properties of the three-dimensional supersymmetric quantum electrodynamics. The theory is shown to be finite at all loops orders in a particular gauge. We also present a perturbative analysis of the supersymmetric Chern-Simons model coupled to a Higgs field. We study the spontaneous symmetry breaking of the U(1) gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level. We also verify that when coupled to a massless scalar superfield, the supersymmetric Chern-Simons model present dynamical generation of mass, a mechanism that in D = 2 + 1 spacetime dimensions, differently from the four-dimensional non-supersymetric model (Coleman-Weinberg), only occurs from two-loop order. Some other related results are also enclosed in this thesis, such as a study of the supersymmetric noncommutative CP**(N-1) model and the equivalence between Maxwell-Chern-Simons and Self-Dual supersymmetric models. In whole work, supersymmetry is manifest.

Através do formalismo de supercampos, estudamos as propriedades ultravioletas da eletrodinâmica quântica supersimétrica no espaço-tempo tridimensional. Mostramos que esta teoria é finita em todas as ordens de perturbação num calibre particular. Também apresentamos uma análise perturbativa do modelo de Chern-Simons supersimétrico acoplado a um supercampo escalar complexo. Com isso, estudamos a quebra da simetria de calibre U(1) e calculamos as primeiras correções quânticas à ação efetiva na fase quebrada. Mostramos que a renormalização da equação de gap é suficiente para assegurar a renormalizabilidade do modelo em um laço de aproximação. Nós também verificamos que quando acoplado a um supercampo escalar sem massa, o modelo de Chern-Simons supersimétrico apresenta geração dinâmica de massa, um mecanismo que em D = 2 + 1 dimensões do espaço-tempo, diferentemente do modelo não-supersimétrico quadridimensional (Coleman- Weinberg), só ocorre a partir da aproximação de dois laços. Alguns outros resultados relacionados são também incluídos nesta tese, tais como um estudo do modelo CP**(N-1) não-comutativo supersimétrico e a equivalência entre os modelos de Maxwell-Chern-Simons e Auto-Dual supersimétricos. Em todo nosso trabalho, supersimetria é manifesta. / Within the superfield formalism, we study the ultraviolet properties of the three-dimensional supersymmetric quantum electrodynamics. The theory is shown to be finite at all loops orders in a particular gauge. We also present a perturbative analysis of the supersymmetric Chern-Simons model coupled to a Higgs field. We study the spontaneous symmetry breaking of the U(1) gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level. We also verify that when coupled to a massless scalar superfield, the supersymmetric Chern-Simons model present dynamical generation of mass, a mechanism that in D = 2 + 1 spacetime dimensions, differently from the four-dimensional non-supersymetric model (Coleman-Weinberg), only occurs from two-loop order. Some other related results are also enclosed in this thesis, such as a study of the supersymmetric noncommutative CP**(N-1) model and the equivalence between Maxwell-Chern-Simons and Self-Dual supersymmetric models. In whole work, supersymmetry is manifest.

Neste trabalho, apresentamos um método que permite explicitar a arbitrariedade contida nas soluções das equações de onda relativísticas, na presença de certos tipos de campos eletromagnéticos externos. Esta arbitrariedade está relacionada com a existência de uma transformação, com a qual podemos reduzir o número de variáveis presentes na equação original. Através desta transformação, criamos uma representação, a qual permite obter novos conjuntos de soluções exatas e construir a função de evolução para a equação de Klein-Gordon. Como resultado, apresentamos novos conjuntos de soluções, estacionárias e não-estacionárias, para o problema em um campo magnético constante e uniforme e a combinação deste campo com um campo elétrico longitudinal. / We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest, and to construct the evolution function to the Klein-Gordon equation. As resulted, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.