Mathematics to Understand String Theory/SuperString

• Studying
• wyattbohr
In summary, for learning about string theory and quantum mechanics, I would recommend reading books about quantum field theory and general relativity, and also studying functional analysis, Lie theory, and a bit of abstract algebra of graded Lie algebras.

wyattbohr

I just recently graduated with a mathematics degree. Lately, I've been very fascinated with quantum mechains and string theory, but when I try to do research I am a little overwhelmed by all the varying topics of advanced mathematics I have to know. Can anyone suggest mathematical topics to teach myself to better understand string theory and quantum mechanics? Thank you :)

wyattbohr said:
I just recently graduated with a mathematics degree. Lately, I've been very fascinated with quantum mechains and string theory, but when I try to do research I am a little overwhelmed by all the varying topics of advanced mathematics I have to know. Can anyone suggest mathematical topics to teach myself to better understand string theory and quantum mechanics? Thank you :)
I would say: functional analysis, Lie theory and a bit abstract algebra of graded Lie algebras.

From a mathematical point of view, I have a book about "Supermanifolds and Virasoro Algebras", unfortunately I don't know whether an English version exists.

I don't know string theory, but I was once an invited speaker at a conference for people who wanted to learn my subject for use in string theory. I got the impression that Riemann surfaces is a key topic in that area. Indeed "strings" are apparently essentially Riemann surfaces. Here is a reference to the proceedings of that conference, which are somewhat scarce, but may be in libraries.
(I gave away my own copy when I moved.

https://www.amazon.com/dp/9971509032/?tag=pfamazon01-20

The book I used for this is Nakahara:

https://www.amazon.com/dp/0750306068/?tag=pfamazon01-20

This is in my experience the best book to look for; it also contains some topics on QM. But the basis for doing string theory is Quantum Field Theory and General Relativity (and all the accompanying math). If you don't master these topics, string theory is way out of your league.

To get an idea, the most approachable book on string theory is Zwiebach. But also be aware that it's very thorough about a lot of stuff which is skipped by more advanced texts. Topics like conformal field theory or supersymmetry are not or barely touched.

1. What is String Theory/SuperString?

String Theory/SuperString is a theoretical framework in physics that attempts to reconcile general relativity and quantum mechanics by describing the fundamental building blocks of the universe as tiny, vibrating strings.

2. How does mathematics play a role in understanding String Theory/SuperString?

Mathematics is crucial in understanding String Theory/SuperString as it provides the necessary tools and language to describe the complex interactions and behavior of these tiny strings. It involves advanced mathematical concepts such as differential geometry, topology, and algebraic geometry.

3. What are the main mathematical concepts used in String Theory/SuperString?

Some of the main mathematical concepts used in String Theory/SuperString include differential equations, group theory, and complex analysis. These concepts help to describe the properties and behavior of strings and their interactions.

4. How does String Theory/SuperString relate to other areas of mathematics?

String Theory/SuperString has connections to various areas of mathematics such as topology, algebraic geometry, and number theory. It also incorporates concepts from other areas of physics, such as quantum mechanics and general relativity.

5. What are some of the challenges in using mathematics to understand String Theory/SuperString?

One of the main challenges in using mathematics to understand String Theory/SuperString is that it involves highly complex and abstract mathematical concepts, making it difficult for non-mathematicians to grasp. Additionally, there is still much research and development needed to fully understand and prove the validity of String Theory/SuperString.