Learning Point Group Theory: Challenges of Lee Groups

In summary, Georgi's "Lie Algebras in Particle Physics" is a good reference for learning about Lie Groups. Sternberg's "Group Theory and Physics" is a good reference if you're interested in understanding Lie Groups from a modern perspective.
  • #1
zwoodrow
34
0
Hi Everyone,
Back in college i informally learned what i would call point group theory. Most of it never touched on continuous transformations. When I learned it back then it was all pretty straight forward. Recently I have been trying to learn about Lee groups (to understand symmetries in Lagrangians in field theory), however whenever I pick up a book or tutorial its like hitting a wall- it doesn't seem like group theory at all. Does anyone have a good book or tutorial or video to recommend?
I appreciate any input.
thanks
doug
 
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  • #2
It's actually spelled 'Lie Group'. Maybe that's why you couldn't find any good refs ;)?

One good reference is Georgi's "Lie Algebras in Particle Physics" -- obviously the treatment is developed towards particle theory, but the beginning chapters are generally helpful.
 
  • #3
thank you, oh dear god i am going to be crucified by all of the nerds for that one.
 
  • #4
Yeah, you know, I'd like to offer some words of encouragement, but they're going to destroy you :biggrin:
 
  • #5
Because it's not the same guy as Bruce Lee, you know.
 
  • #6
Schutz's "Geometrical Methods of Mathematical Physics" has a quite gentle introduction. I'd recommend it.
 
  • #7
Sternberg, "Group Theory and Physics". It's quite an unusual but very elegant book. He does not only treat Lie Groups but also point groups and permutation groups, from a very modern point of view.
However, there are loads of typos.
 
  • #8
Well I used a textbook by Brian Hall (search for his name and you'll find the textbook).

It's an easy going textbook with minimal prequisites, though I would recommend having taken a course in topology and knowledge of manifold theory to some extent.

All the beckground knowledge needed to read the bulk of the book is in the appendices.
My critic is partial cause I haven't read all through it, perhaps next year accompanied with a course can be a good start.

Cheers.
 
  • #9
Lecture notes at http://webusers.physics.illinois.edu/~m-stone5/mmb/mmb.html [Broken]
 
Last edited by a moderator:

1. What is Point Group Theory?

Point Group Theory is a branch of mathematics that deals with the symmetry properties of objects in different dimensions. It is used to classify and study the symmetries of molecules, crystals, and other geometric structures.

2. What are Lee Groups?

Lee Groups are a type of mathematical group that is used in Point Group Theory to describe symmetries in continuous spaces. They are named after mathematician T. D. Lee and are an important tool in understanding the symmetries of physical systems.

3. What are the challenges of studying Lee Groups?

One of the main challenges of studying Lee Groups is the complexity of the mathematical concepts involved. It requires a strong background in advanced mathematics, as well as a deep understanding of abstract algebra and topology. Additionally, the application of Lee Groups to physical systems can be difficult and requires careful analysis.

4. How is Point Group Theory used in chemistry?

In chemistry, Point Group Theory is used to classify molecules and predict their properties based on their symmetry. It is also used to explain and understand chemical reactions, as well as to design new molecules with specific properties.

5. What are some real-world applications of Point Group Theory and Lee Groups?

Point Group Theory and Lee Groups have many practical applications in fields such as chemistry, physics, materials science, and engineering. They are used to study the properties of crystals and other materials, to understand the behavior of molecules and chemical reactions, and to design new materials with specific properties. They are also used in computer graphics and robotics for building models and simulations of complex systems.

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