Introduction to Quantum Group Theory for College Math Majors

In summary, the conversation discusses the need for a good introduction to quantum group theory for someone with prior knowledge of group theory. The intended audience is college math majors and the goal is to apply group theory to quantum mechanics. Suggestions for resources, including a book by Howard Georgi and a thread on Physics Forums, are given.
  • #1
Soveraign
55
0
I'm looking for a good introduction on quantum group theory for someone who has already had a semester class on group theory. I'll be putting together a short paper (5 pages) on the topic with the intended audience of college math majors. My naive understanding is that symmetry and interaction properties of subatomic particles can be modeled using special kinds of groups. I need a resource that can help me take the step from simple groups you study in a math course to how one can apply them to quantum mechanics (simple examples would be great too).

Any help is appreciated!

Brian
 
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  • #2
Great idea you have here !
A major book in this context :
Howard Georgi, "Lie Algebras in Particle Physics" Addison Wesley Frontiers in Physics Series.
 
  • #4
Thanks for the pointers! Some of those resources are about the level I'm looking for.

Brian
 

1. What is quantum group theory?

Quantum group theory is a branch of mathematics that studies the algebraic structures called quantum groups. These groups are generalizations of classical groups and have applications in theoretical physics, mathematical physics, and algebraic geometry.

2. What are the prerequisites for studying quantum group theory?

The main prerequisites for studying quantum group theory are a strong foundation in linear algebra, abstract algebra, and group theory. Some knowledge of topology and functional analysis may also be helpful.

3. How is quantum group theory different from classical group theory?

Quantum group theory differs from classical group theory in several ways. One major difference is that quantum groups are non-commutative, meaning that the order in which operations are performed matters. Additionally, quantum groups have a different set of axioms and properties compared to classical groups.

4. What are the applications of quantum group theory?

Quantum group theory has numerous applications in various fields such as theoretical physics, mathematical physics, and algebraic geometry. It has been used to study quantum mechanics, quantum field theory, and knot theory, among others.

5. How can quantum group theory be applied to real-world problems?

Quantum group theory can be applied to real-world problems by providing a mathematical framework for understanding and analyzing physical phenomena. It has been used to model and solve problems in quantum computing, quantum cryptography, and quantum information theory.

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