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I'm in the process of looking for a PhD position in Theoretical Physics but I'm unclear about a few things.

1) I still don't really know what I really want to do. The only thing I am sure of is that I want my research to help me in my understanding of ideas which I regard as crucial to working out my "view of the world", so to speak. I want to develop a deep understanding of QM and QFT and I am more interested in foundational issues. (with a future in string theory or other advanced field a definite option, but I feel that right now I need to strengthen this "basic knowledge" and would not enjoy jumping into 11 dimensions without properly seeing the present 4 :D )

I enjoy, for instance, the work of Arnold on ODEs and Classical Mechanics, because the underlying mathematical structure makes the topics so much clearer! My undergraduate courses in QM, for instance, were all willy nilly: we were calculating relativistic corrections to molecules without having done a) any functional analysis courses at all and b) no serious course in relativity, a situation I really did not enjoy. Later courses in QFT and GR didn't fare much better. I only recently came to understand how a Fock space is constructed and a course in differential geometry cleared up what goes on in GR.

Having said that, I would ideally like to work in a field where foundational questions (such as the nature of mappings between spaces, operator spectra etc..) can have a direct impact on applications. Is there such a beast? Here's the reason for my stance: My master thesis was a theoretical project to compute instanton transition probabilities in a solid state system. I now know that it would have benefitted immensely from a study of the underlying mathematics (overdefined systems) and would have, perhaps, yielded usable results...

2) I'm aware of the application procedures at Dutch and UK universities and haven't yet found any positions that would truly strike my interest. However, I am not sure how to approach applications in other European countries as there are no "lists of open PhD positions". Should I just randomly contact researchers the work of whom I find interesting? Should I include the whole range of application materials on first contact or just a short resume of my interests and a request for more information? Are researchers in e.g. Germany entitled to creating PhD positions if they have an interesting candidate? Do departments across Europe have personnel that would be ready to help a struggling searcher such as myself to find a home?

Thanks in advance for any and all replies,

BK