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The first part deals with lattice approach to field theories. The fermion doubling problems are described. This doubling can be removed if a dual lattice is introduced, as first pointed out by Stacey. His method is developed and in the process a formalism for the construction of a covariant difference lattice operator and thus of a gauge invariant action, is exhibited. It is shown how this formalism relates to the work of Wilson. Problems of gauge invariance can be traced back to the absence of the Leibnitz rule on the lattice. To circumvent this failure the usual notion of the product is replaced by a convolution. The solutions display a complementarity : the more localised the product the more extended is the approximation to the derivative and vice-versa. It is found that the form of the difference operator in the continuous limit dictates the formulation of the full two-dimensional supersymmetric algebra. The construction of the fields necessary to form the Wess-Zumino model follows from the requirement of anticommutativity of the supersymmetric charges. In the second part, the Skyrme model is reviewed and Bogomolnyi conditions are defined and discussed. It appears that while the Skyrme model has many satisfactory features, it fails to describe the interactions between nucleons correctly. These problems are brought out and the available solutions reviewed.

Thesis (Honors)--College of William and Mary, 2008. / Includes bibliographical references (leaves 19-20). Also available via the World Wide Web.

Thesis (Ph. D.)--University of North Texas, August, 2008. / Title from title page display. Includes bibliographical references.

Honors thesis (B.A.)--Ithaca College Dept. of Mathematics, 2009. / "May 2009." Includes abstract and bibliographical references (p. 40) Print copy also available in the Ithaca College Archives

Thesis (Ph. D.)--University of Pennsylvania, 1938. / Published also without thesis note.

Thesis (M. Phil.)--University of Hong Kong, 1998. / Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

O movimento de três partículas idênticas e sem spin em uma dimensão é o objeto de estudo neste trabalho. As equações de Faddeev que descrevem o espalhamento de uma partícula por um estado ligado de duas partículas é estudado extendendo-se analiticamente um dos momentos para todo o plano complexo (chamado de método de Brayshaw). Encontramos que quando um subsistema de duas partículas apresenta um estado ligado com energia V0, o sistema de três partículas correspondente apresentará um estado ligado com energia 4 V0. Também concluímos que se um subsistema de duas partículas apresenta uma ressonância para uma energia V0, o mesmo não ocorre no sistema de três partículas. Estes resultados resolvem uma longa controvérsia na literatura. / The one dimension motion of three identical spinless particles is studied here. The Faddeev equations describing the scattering of one particle by a two particle bound-state is studied by extending analytically one of the momenta to the whole complex plane (Brayshaw\'s method). It is found that to a bound-state of energy V0 in the two particle subsystem corresponds a bound-state of energy 4V0 in the three particle system. It is also found that if the two particle subsystem has a resonance pole at V0 it does not follows that there is .a resonance in the three particle system. These results solve a long standing controversy in the literature.

The action principle of field theory, usually applied only to linear theories, such as electrodynamics, is shown to be useful in the nonlinear theory of magnetohydrodynamics The well-known conservation laws are derived by utilization of invariance properties of the appropirate lagrangian In addition, a set of new conservation laws, corresponding to generalizations of the Helmholtz vortex theorem in hydrodynamics, are obtained by exploiting a certain type of gauge invariance of the magnetohydrodynamical action integral A number of formal simplifications are introduced which suggest themselves through the action principle Three problems which illustrate the resulting formulation of magnetohydrodynamics are discussed / Science, Faculty of / Physics and Astronomy, Department of / Graduate