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Mathematical methods of String Theory

  1. May 3, 2006 #1
    Wasn't really sure where to put this question as it is not really an academic or career question and since it about String Theory, I thought I should put it here. I was wondered what type of math I need to know to read an introductory course on string theory. I'm going through a mathematical expidition, with hopes that I can avoid topology courses and numerical analysis in my study of physics. However, String Theory looks it uses heavily applied topology. Since I really want to study this theory, I may just have to actually study these subjects- unless you guys can tell me differently. I'm sure that even Classical physics be understood better with topology, I just want to know if it is logical to give a course in String Theory without thorough knowledge of topology. Would it be like giving an introductory course in General Theory without expecting thorough knowledge of Groups?
  2. jcsd
  3. May 4, 2006 #2
  4. May 4, 2006 #3


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    These are excellent guides, but the third one only goes up to noncommutative geometry. I think the cutting edge now requires also higher category theory (topos, 2-categories, etc.). And I would also suggest modern integrability theory (Lax Pairs, etc.), but that is just a personal notion. An important point is that the space of things to learn is expanding faster than the subset one's mastered material can. Hence spacialization, even within a single field such as string theory.
  5. May 4, 2006 #4
    You're right self adjoint. The range of mathematical subjects that need to be mastered at some depth is quite daunting, even for a mathematican.

    John G.
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