Mathematical methods of String Theory

[Evilinside]

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?

 

[FSC729]

Superstringtheory.com has a list of the mathematical subjects you will need to learn:

http://www.superstringtheory.com/math/math1.html

http://www.superstringtheory.com/math/math2.html

http://www.superstringtheory.com/math/math3.html

Good Luck

John G.

 

[selfAdjoint]

Superstringtheory.com has a list of the mathematical subjects you will need to learn:

http://www.superstringtheory.com/math/math1.html

http://www.superstringtheory.com/math/math2.html

http://www.superstringtheory.com/math/math3.html

Good Luck

John G.

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.

 

[FSC729]

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.