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This thesis investigates the problems within quantum mechanics for the Bohm model caused by Lorentz invariance and the existence of photons. A model describing the electromagnetic interactions of fermions is produced which does not use photons and avoids these problems. It is then shown how these techniques can be extended to linearised gravitational interactions. Finally semi-classical gravity and the possibility of gravitationally induced collapse are considered. In the first part of the thesis two modifications to the Bohm model are proposed. One takes account of Lorentz invariance, and the other is capable of describing photons. The main part of the thesis is devoted to describing interactions in a way which does not need extra gauge particles, and so is in the same spirit as the Bohm model. Electromagnetic interactions are formed using a 4-potential operator which is calculated directly, without imposing commutation relations on the 4-potential. This leads to an expression for the 4-potential in terms of the Dirac field, and results in there being no photon states. There are various ways of constructing the theory and the scattering matrix of standard QED is compared to the scattering matrix of the version which appears to be most similar. Considering only the matrix elements between fermion states, they are found to be in agreement at the order e(^2), but disagree at the order e(^4). It follows that this model, which otherwise appears to be a self consistent theory of QED, cannot agree with experiment. The same techniques can be used to quantise General Relativity when it is linearised about the Minkowski metric. The metric operator is calculated in terms of the Dirac field. The interaction is similar to that of electrodynamics, being of order 4 in the Dirac field. Finally issues relating to gravitational collapse are discussed.

The handling of topological aspects in boundary value problems of engineering electromagnetics is often considered to be an engineer's art and not a science. This thesis is an attempt to show that the opposite is true. Through the use of differential forms and rudimentary concepts from homology theory a paradigm variational boundary value problem is formulated and investigated. It is seen that reasoning in terms of the Tonti diagram for this problem may lead to false conclusions if cohomology groups are ignored. As a prelude to this investigation, a suitable orthogonal decomposition of differential forms is derived and the roles played by the long exact homology sequence and topological duality theorems for compact orientable manifolds with boundary are considered in detail.

Through a holographic recording a property from the third dimension, the depth, is obtained in the form of a phase map of the incident light. One wavelength holography will have a unique phase for the depth range corresponding to the wavelength of the light and outside this range the real depth can not be resolved. By introducing more wavelengths to the measurement the unique phase combination of the waves will have a wider range and larger objects can be resolved. Up to six wavelengths can be simultaneous recorded by making them occupy different spatial frequencies. A set of spatial frequencies together describing a property of the wave is referred to as a lobe. For more than 6 wavelengths and a larger depth range produced by a more seldom repeated unique phase combination the individual waves will occupy the same frequencies, i.e. the lobes overlap. The separation of overlapping lobes is essential in order to make precise and time independent measurements of large and/or moving objects. To separate the lobes the complex fields, i.e. the phases together with the amplitudes, were simulated to propagate a distance and again recorded. The propagation leads to a phase shift of the spatial frequencies which reveals the complex fields in the case of two overlapping wavelengths. For three overlapping wavelengths the resolution, i.e spatial frequencies describing the object, has to be reduced in order to determine the individual complex fields. Since the propagation is a linear transformation for the frequencies that do not overlap, only the overlapping elements whose propagation is nonlinear produce new information. The new information gained is therefore independent of the number of wavelengths used which limits the exact determination of the fields to two wavelengths. Through the holographic recording another property of the complex field is obtained which is the superimposed individual intensities. This bounds the complex fields to certain values, i.e. restricts the possible amplitude of the waves. The recording in the two planes produces two intensity distributions which both must be satisfied by the complex fields. The optimization model for this was formulated and a simple optimization algorithm was implemented. Instead of an equality constraint of the intensities the inequality constraint was implemented, mainly due to that the optimization process was out of the scope of the thesis and the inequality constraint resulted in a simple implementation. The result pointed out important properties even though the optimization could not separate the fields satisfactorily for more than three wavelengths. The inequality constraint contains enough information to solve the case of three overlapping wavelengths.

Thesis (Ph.D.)--McMaster University, 2002. / Advisors: Dr. John Litva, Dr. Ke-Li Wu. Includes bibliographical references (leaves 106-115). Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2002. / Advisors: Dr. John Litva, Dr. Ke-Li Wu. Includes bibliographical references (leaves 106-115). Also available via World Wide Web.

Thesis (M.S.)--Ohio University, August, 1989. / Title from PDF t.p.

Thesis (PhD) - Swinburne University of Technology, Brain Sciences Institute, 2007. / Doctorate of Philosophy, Brain Sciences Institute, Swinburne University of Technology - 2007. Typescript. "April 2007".