McCauley, Joseph L., Jr.2022-08-312022-08-31197819784385411https://hdl.handle.net/10657/10881The classical dielectric function has been studied extensively in the Random Phase Approximation (RPA), which yields the Debye-Huckel result. The present work extends the accuracy of the calculations beyond the RPA for a charged particle medium of either one component (with an oppositely charged 'jellium' background) or two components of opposite charge. The calculations will be carried out in one, two, and three dimensions, with particular emphasis on the two dimensional results. Numerical values of the dielectric function will be obtained for the second order results (the RPA values are referred to as the first order results). Surprisingly, these values differ only slightly between the dimensions for a given value of a particular parameter within the region of applicability. A diagrammatic method is also developed to provide a systematic procedure for approaching higher order results.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital