Mathematical methods of String Theory

In summary, you will need to learn mathematics subjects like mathematics 1, mathematics 2, and mathematics 3 to understand introductory course on string theory.
  • #1
Evilinside
20
0
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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  • #2
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.
 
  • #3
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.
 
  • #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.
 

What is String Theory?

String Theory is a theoretical framework in physics that attempts to explain the fundamental nature of the universe. It proposes that the fundamental building blocks of the universe are not particles, but tiny, vibrating strings.

Why is String Theory important?

String Theory is important because it attempts to unify the two major theories of physics, general relativity and quantum mechanics. It also has the potential to provide a deeper understanding of the fundamental laws of the universe and potentially solve some long-standing problems in physics.

What are the mathematical methods used in String Theory?

The mathematical methods used in String Theory include differential geometry, algebraic geometry, topology, and group theory. These methods are used to describe the behavior of strings in different dimensions and to make predictions about the properties of the universe.

Can String Theory be tested experimentally?

Currently, there are no experimental tests that can directly confirm or refute String Theory. However, some predictions of String Theory, such as the existence of extra dimensions, may be testable through experiments at high-energy particle colliders.

What are the criticisms of String Theory?

One criticism of String Theory is that it has not yet been confirmed by experimental evidence. Other criticisms include the complexity of the theory and the fact that it has yet to make testable predictions that can be validated. Additionally, some argue that it is not a complete theory and may need to be combined with other ideas in order to fully explain the universe.

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