Theses and Dissertations

Date of Award

5-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Karen Yagdjian

Second Advisor

Dr. Sergey Grigorian

Third Advisor

Dr. Anahit Galstyan

Abstract

It is the ambition of this thesis to analyze in a concise and coherent manner the idiosyncratic nature of partial differential equations and their mathematical structure in distinct curved spacetimes. In our work special interest is taken in quantum fields dwelling within the de-Sitter geometry. In Chapters I, II, III, and IV, a meticulous study of general relativity is undertaken with one of its solutions derived, an introduction of quantum mechanics is posed, the relativistic quantum theory of fermions is defined, and a “merging” of the former chapters and results are considered, respectively. With what has been derived we seek to examine the paradigm of the Dirac equation in the de-Sitter spacetime. We determine the vierbein, its dual, and the spin connection of the metric under consideration in order to define the Dirac equation in the de Sitter geometry. Once achieved we seek to redefine the former in Klein-Gordon form such that we may derive an analytic solution to the novel equation. Inevitably, the physical ramifications of said solution will detail the behavior of a relativistic fermion traversing through the de Sitter geometry.

Comments

Copyright 2020 Jorge A. Garcia. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/partial-differential-equations-curved-spacetimes/docview/2451427973/se-2?accountid=7119

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