Made available in DSpace on 2014-06-11T19:25:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-12-18Bitstream added on 2014-06-13T20:07:32Z : No. of bitstreams: 1 calixto_ap_me_sjrp.pdf: 2312676 bytes, checksum: 5de410aa23e48f51d5aa6d67e78c03b6 (MD5) / Nesta dissertação é apresentada uma aproximação da Teoria de Variáveis Complexas de duas para quatro dimensões. Procura-se definir diferenciabilidade de funções quaterniônico, a partir da qual se estabelece uma relação com a teoria de regularidade de funções hipercomplexos [9]. Observa-se que após definir o operados quaterniônico T, é possível reescrever equações clássicas da Física de forma concisa, utilizando a definição de regularidade, que resulta na decomposição de uma equação diferencial de segunda ordem em duas equações diferenciais lineares de primeira ordem.

This thesis is a critical study of Lord Byron's poetic drama, Cain. Most critics in the past have seen the work as a personal statement of religious skepticism on the part of Lord Byron, and hence as an out-and-out attack on traditional, Christian doctrine. With this preconception in mind, they have concerned themselves with pointing out attitudes and ideas in the play which may be said to be antithetical to the Christian world view, and they have then assessed the play simply in these terms. It is the contention of this paper that this presupposition has led the critics away from the realm of meaning intended by Lord Byron, and that a proper understanding of the play can only arise from a full, critical study of the central issue with which this "metaphysical" drama is concerned. The method followed is to analyse the differences in form, structure and argument between two accounts of this story - that found in the Bible, and Byron's poetic drama - on the assumption that such radical changes as we shall note are essential to the conveyance of Byron's peculiar meaning, and that a study of them must reveal the proper coherence and unity of Byron's work. We shall see that Cain is not a mere recounting of this story, but rather that it is a reconceptualization of the predicament facing Adam and Eve and the first family, structured so as to focus upon the human situation, so chat in the work Byron is not concerned with religious values, but with human values; not concerned to advance or refute traditional, religious concepts, but to reveal his insights into the common, human predicament. / Arts, Faculty of / English, Department of / Graduate

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This thesis discusses the Ruijsenaars-Schneider model and its connection to Calogero-Moser systems and the sine-Gordon equation. The derivations and mathematical framework presented aims at making the model comprehensible to non-experts in the field. Two different methods, the Bäcklund transformation and Ruijsenaars-Schneider model, are used to find soliton solutions to the sine-Gordon equation.

Speculations in the signicance of retardation aects in fundamental physics, especiallythe Dirac equation, that Atiyah and Moore bring up in "A shifted view of fundamental physics" are summarized and reviewedin terms of basic undergraduate conceptions. Some remarks are further investigated and ashifted version of the Klein Gordon equation is derived.

The goal of this Thesis is to give a presentation of some key issues regarding the non-perturbative renormalization of the periodic scalar field theories. As an example of the non-perturbative methods, we use the differential renormalization group approach, particularly the Wegner-Houghton and the Polchinski renormalization group equations, in order to investigate the renormalization of a one-component periodic scalar field theory. The Wegner-Houghton equation provides a resummation of the loop-expansion, and the Polchinski equation is based on the resummation of the perturbation series. Therefore, these equations are exact in the sense that they contain all quantum corrections. In the framework of these renormalization group equations, field theories with periodic self interaction can be considered without violating the essential symmetry of the model: the periodicity. Both methods - the Wegner-Houghton and the Polchinski approaches - are inspired by Wilson's blocking construction in momentum space: the Wegner-Houghton method uses a sharp momentum cut-off and thus cannot be applied directly to non-constant fields (contradicts with the "derivative expansion"); the Polchinski method is based on a smooth cut-off and thus gives rise naturally to a "derivative expansion" for varying fields. However, the shape of the cut-off function (the "scheme") is not fixed a priori within Polchinski's ansatz. In this thesis, we compare the Wegner--Houghton and the Polchinski equation; we demonstrate the consistency of both methods for near-constant fields in the linearized level and obtain constraints on the regulator function that enters into Polchinski's equation. Analytic and numerical results are presented which illustrate the renormalization group flow for both methods. We also briefly discuss the relation of the momentum-space methods to real-space renormalization group approaches. For the two-dimensional Coulomb gas (which is investigated by a real-space renormalization group method using the dilute-gas approximation), we provide a systematic method for obtaining higher-order corrections to the dilute gas result.

Proefschrift--Utrecht. / "Stellingen": [4] p. laid in.

Thesis (M.A.)--Carleton University, 2000. / Includes bibliographical references.