Research Orthogonal Lie Group for Physics Applications

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Discussion Overview

The discussion revolves around the exploration of Orthogonal Lie Groups and their applications in physics, particularly for individuals with limited background in group theory. Participants share resources and suggest approaches for understanding the mathematical concepts and their relevance to physical theories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses a desire to start researching Orthogonal Lie Groups and mentions Arfken's book as a potential resource, despite lacking prior knowledge in group theory.
  • Another participant suggests WuKi Tung's book as a suitable starting point but cautions that it may be challenging without a background in group theoretical methods.
  • A different participant recommends Greiner's book on "QM -- Symmetries" for understanding the basic mathematics in the context of quantum theory, noting its relevance to orthogonal groups in relativity.
  • One participant questions the necessity of studying extensive material, seeking a concise application of orthogonal Lie groups in physics.
  • Another participant responds that a simple application, such as conservation of angular momentum, could be provided but emphasizes that a deeper understanding of Lie groups requires extensive study across multiple textbooks.

Areas of Agreement / Disagreement

Participants generally agree on the need for foundational study in group theory to understand its applications in physics. However, there is no consensus on the best approach or specific resources, as different participants suggest various texts and express differing views on the amount of study required.

Contextual Notes

Some participants highlight the challenge of understanding the material without prior coursework in group theory, indicating that assumptions about the reader's background may affect the recommendations given.

Who May Find This Useful

This discussion may be useful for students or individuals interested in the intersection of mathematics and physics, particularly those looking to understand the role of Lie groups in physical theories.

erbilsilik
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[Mentor's Note: Thread moved from homework forums]

Where can I start to research this question? I did not take any course on Group theory before and I know almost nothing about the relationship with this pure maths and physics. I've decided to start with Arfken's book but I'm not sure.


1. Homework Statement

Orthogonal Lie Group and the application of this group in physics

Homework Equations

The Attempt at a Solution



http://www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
 
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WuKi Tung's book is a good place to start from a physics stand point, but without a background in group theoretical methods, it will be a tough read.
 
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erbilsilik said:
Where can I start to research this question? I did not take any course on Group theory before and I know almost nothing about the relationship with this pure maths and physics.
I found Greiner's book on "QM -- Symmetries" quite helpful for acquiring an understanding of the (basic) math in the context of quantum theory. Of course, orthogonal groups are also relevant in relativity and elsewhere, but Greiner's book will get you started. (I found Greiner's series of textbooks especially good for introductory-level self-study since he doesn't skip steps.)
 
So are you saying that I need to study the first 50 page in Greiner's book? I don't have a much time actually, looking for the best recipe for an answer 'one application of ortogonal Lie group in physics'.
 
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Well, when you said you wanted to "research this question", I thought you meant you wanted to acquire an understanding of the use of Lie groups in physics.

If you just want a "best recipe for an answer 'one application of orthogonal Lie group in physics', I could answer: "conservation of angular momentum", which is discussed in any respectable textbook on Classical Mechanics. But I daresay that would just lead to more questions.

You'll need to study a lot more than 50 pages, and from multiple textbooks, if you want to understand how to work with a Lie group. I only mentioned Greiner's book precisely because he got me over the basics in a reasonable amount of time. But yes, you'll have to actually read something, even if it takes a while.
 
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