The initial chapter of the thesis provides a review of Weinberg’s formalism for the derivation of quantum fields. The formalism is extended to allow for the derivation of quantum fields with more than one spin degree of freedom. It is conjectured that it may be possible to construct massive bosonic quantum field theories of any desired spin j that are consistent and unitary at all energies without the need for regulator terms by including j + 1 spin degrees of freedom: j, j - 1, down to j - j. The concept is then demonstrated in two subsequent chapters by the derivation of a quantum field with spin one and spin zero degrees of freedom followed the derivation of a quantum field with spin two, spin one, and spin zero degrees of freedom. Both field theories are found to be consistent and unitary at all energies without the need for regulator terms. The final two chapters are on unrelated topics. The penultimate chapter provides an explicit derivation of quantum fields for massless particles of spin one-half. In the final chapter, a derivation of the free-space Proca and Maxwell equations is provided via a consistent identification of the linear combinations of the classical fields of the (1,0) and (0,1) representations of the orthochronous Lorentz group.

We study the conjectured equivalence between the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under a naive application of the bosonization rules. We start with a review of the equivalence between sine-Gordon model and the massive Thirring model. We study the models by perturbation theory and then determine the equivalence. We find that the dependence of the identifications on the couplings can change according to the definition of the vector current. With the operator identifications of the special case corresponding to a free fermionic theory, known as the bosonization rules, we describe the equivalence between the massless Thirring model and the model of a compactified free boson field. For the massless Thirring model, or equivalently the O(2) Gross-Neveu model, we study the conservation laws for the vector current and the axial current by employing a generalized point-splitting method which allows a one-parameter family of definitions of the vector current. With this parameter, we can make contact with different approaches that can be found in the literature; these approaches differ mainly because of the specific definition of the current that was used. We also find the Sugawara form of the stress-energy tensor and its commutation relations. Further, we rewrite the identifications between sine-Gordon and Thirring models in our generalized framework. For the O(3) Gross-Neveu model, we extend our point-splitting method to determine the exact expression for the supercurrent. Using this current, we compute the superalgebra which determines three quantum components of the stress-energy tensor. With an Ansatz for the undetermined component, we find the trace anomaly and the first beta-function coefficient. The central charge which can be computed without using our point-splitting method is independent of the coupling constant, in fact, it is always zero. For the supersymmetric sine-Gordon model, we review its supersymmetry in the context of models derived from a scalar multiplet in two dimensions. We then obtain the central charge and discover an extra term that was missing in the original derivation. We also analyze how normal ordering modifies the central charge. Finally, we discuss the conjectured equivalence of the O(3) Gross-Neveu model and the supersymmetric sine-Gordon model under the naive application of the bosonization rules. Comparing our results of the central charges and the supercurrents for these models, we find that they disagree; consequently the models should be generically inequivalent. We also conclude that the naive application of the bosonization rules at the Lagrangian level does not always lead to an equivalent theory.

Bibliography: p. 115-120. / v, 141, [26] p. : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1998

Lattice simulations are a popular tool for studying the non-perturbative physics of nonlinear field theories. To perform accurate lattice simulations, a careful account of the discretization error is necessary. Spatial discretization error as a result of lattice spacing dependence in Langevin simulations of anisotropic (2 + 1)-dimensional classical scalar field theories is studied. A transfer integral operator (TIO) method and a one-loop renormalization (1LR) procedure are used to formulate effective potentials. The effective potentials contain counterterms which are intended to suppress the lattice spacing dependence. The two effective potentials were tested numerically in the case of a phi-4 model. A high accuracy modified Euler method was used to evolve a phenomenological Langevin equation. Large scale Langevin simulations were performed in parameter ranges determined to be appropriate. Attempts at extracting correlation lengths as a means of determining effectiveness of each method were not successful. Lattice sizes used in this study were not of a sufficient size to obtain an accurate representation of thermal equilibrium. As an alternative, the initial behaviour of the ensemble field average was observed. Results for the TIO method showed that it was successful at suppressing lattice spacing dependence in a mean field limit. Results for the 1LR method showed that it performed poorly.

The one-loop effective action for N = 2 and N = 4 supersymmetric Yang-Mills theories are computed to order F5; and F6 respectively by the use of heat kernel techniques in N = 1 superspace. The computations are carried out via the introduction of a new method for computing DeWitt-Seeley coefficients in the coincidence limit. To order F5, the bosonic components of both N = 2 and N = 4 supersymmetric Yang-Mills theories are extracted and compared with the existing literature. For N = 4 super Yang-Mills theories the F5 terms are found to be consistent with the non-Abelian Born-Infeld action computed to this order by superstring methods and various other means of computing deformations of supersymmetric Yang-Mills theory. The result proved to be the final piece of a puzzle, leaving little doubt that there exists a unique deformation of maximally symmetric super Yang-Mills theories at this order. The F6 terms will be of importance for comparison with superstring calculations, including direct tests of the AdS/CFT conjecture. The bosonic components of N = 2 supersymmetric Yang-Mills are also shown to be consistent with existing literature, and will be of importance for testing of generalizations of the AdS/CFT conjecture.

Thesis (Ph.D.)--York University, 2006. Graduate Programme in Earth and Space Science. / Typescript. Includes bibliographical references (leaves 86-90). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19789

Thesis (Ph.D) -- Australian National University, 2007. / DVD contains movies in .mov (macintosh quicktime) and .mpg formats, providing additional visualisation of the material discussed in the thesis. It also contains the source files for figures within the thesis as well as sample numerical code that was used for the research. The accompanying .txt files provide a brief description of the movie and a link to the relevant part of the thesis. Also contains some files in pdf format.

Thesis (Ph.D.)--York University, 2007. Graduate Programme in Physics and Astronomy. / Typescript. Includes bibliographical references (leaves 211-217). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR29346

Thesis (Ph. D.)--Oregon State University, 1999. / Typescript (photocopy). Includes bibliographical references (leaves 60-61). Also available on the World Wide Web.

Thesis (Ph. D.)--University of Texas at Austin, 2003. / Supervisors: Philip J. Morrison and Matthew W. Choptuik. Vita. Includes bibliographical references. Also available from UMI.