Learning Point Group Theory: Challenges of Lee Groups

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Discussion Overview

The discussion centers around the challenges of learning Lie group theory, particularly in the context of understanding symmetries in Lagrangians in field theory. Participants share resources and recommendations for books and tutorials that may aid in this learning process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty transitioning from point group theory to Lie groups, feeling that the latter is not as straightforward.
  • Another participant corrects the spelling of "Lee" to "Lie" and suggests Georgi's "Lie Algebras in Particle Physics" as a helpful reference, noting its focus on particle theory.
  • A different participant recommends Schutz's "Geometrical Methods of Mathematical Physics" for its gentle introduction to the topic.
  • Another suggestion is Sternberg's "Group Theory and Physics," which covers Lie groups, point groups, and permutation groups, though it is noted that the book contains many typos.
  • One participant mentions a textbook by Brian Hall, describing it as accessible with minimal prerequisites, but suggests familiarity with topology and manifold theory would be beneficial.
  • Lecture notes from a specific URL are shared as an additional resource.

Areas of Agreement / Disagreement

Participants generally agree on the challenges of learning Lie group theory and share various resources, but there is no consensus on a single best reference or approach, reflecting a range of perspectives and experiences.

Contextual Notes

Some resources mentioned may have limitations such as typos or varying levels of prerequisite knowledge required, which could affect their accessibility for learners.

Who May Find This Useful

Individuals interested in advanced topics in physics, particularly those studying field theory and symmetries, as well as students transitioning from discrete to continuous group theory.

zwoodrow
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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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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.
 
thank you, oh dear god i am going to be crucified by all of the nerds for that one.
 
Yeah, you know, I'd like to offer some words of encouragement, but they're going to destroy you :biggrin:
 
Because it's not the same guy as Bruce Lee, you know.
 
Schutz's "Geometrical Methods of Mathematical Physics" has a quite gentle introduction. I'd recommend it.
 
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.
 
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.
 
Lecture notes at http://webusers.physics.illinois.edu/~m-stone5/mmb/mmb.html
 
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