Mathematical methods of String Theory

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Discussion Overview

The discussion revolves around the mathematical prerequisites for studying string theory, particularly focusing on the types of mathematics required and the potential necessity of topics like topology and numerical analysis. Participants explore the implications of these requirements on the feasibility of taking introductory courses in string theory.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about the necessity of topology for understanding string theory, questioning whether it is logical to teach string theory without thorough knowledge of topology.
  • Another participant references a resource (superstringtheory.com) that lists mathematical subjects needed for string theory, suggesting that these guides are helpful but may not cover all current requirements.
  • A later reply indicates that the mathematical landscape for string theory is evolving, proposing that higher category theory and modern integrability theory may also be relevant, although this is presented as a personal opinion.
  • One participant acknowledges the daunting range of mathematical subjects required, noting that even mathematicians find it challenging to master these topics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of specific mathematical topics for studying string theory. There are multiple competing views regarding the sufficiency of existing resources and the evolving nature of required mathematical knowledge.

Contextual Notes

Limitations include the lack of clarity on which mathematical subjects are absolutely essential versus those that may enhance understanding, as well as the evolving nature of the field which may introduce new requirements over time.

Evilinside
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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?
 
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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.
 
FSC729 said:
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.
 
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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