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Partial Differential Equations In Curved Spacetimes, Jorge A. Garcia

Theses and Dissertations

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 …