Master Dissertation

Prerequisites
Fixme: Reevaluate the needs as the theory develops.
This is a dissertation for the masters degree in mathematics at the University
of Copenhagen. It is thus the conclusion of 5 years of study. The
thesis is meant to rest on the mathematical fundament the student has obtained
during those years. Clearly, I will not use all the mathematical tools
I am equipped with from the wide variety of disciplines, I been acquainted
with through my studies. It would be more correct to say that it is a narrow
specialization of some of the knowledge I have gained. It is thus difficult
to point out what the prerequisites are, exactly. I will never the less try to
narrow down the fundament on which this thesis rests.
First of all I will emphasize that this thesis is concerned with quantum
electrodynamics. That is, it is concerned with problems arising from both
quantum mechanics and general relativity. Although I will only be concerned
with a few principles of the two, the whole idea and machinery of them are
luring in the background. I have through my studies read several books on
the subjects most important probably being the basic theory to be found in
[7], [8] and [1]. Note that Stone’s Theorem will be taken for granted and
will be normalized.
Also a good deal of functional analysis will be taken for granted. At least
the content of [5]. Especially the theory of distributions will be imperative
the thesis. I will, in some sense, consider the project [4], which I wrote with
my fellow student Morten Bakkedal, as a part of this thesis. The project
covers a good deal of the theory of distributions and wavefront sets resting
on the lecture notes on distributions by Gerd Grubb [2].
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