# Research Orthogonal Lie Group for Physics Applications

• erbilsilik
In summary, you will need to study a lot more than 50 pages to understand how to work with a Lie group and you will also need to read multiple textbooks.

#### erbilsilik

[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

## 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.

erbilsilik
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.

erbilsilik

## 1. What is an orthogonal Lie group?

An orthogonal Lie group is a mathematical object that describes the symmetry of a physical system. It is a group of matrices that preserve a certain geometric structure, such as distance or angles. In physics, these groups are important for understanding the symmetries of physical laws and predicting the behavior of systems.

## 2. How is an orthogonal Lie group used in physics?

Orthogonal Lie groups are used in physics to study the symmetries of physical systems. They can help physicists understand the behavior of particles and fields, and make predictions about their interactions. For example, the special orthogonal group SO(3) is used to describe the rotational symmetries of 3-dimensional space, which is important in understanding the motion of objects in our physical world.

## 3. What are some applications of research on orthogonal Lie groups in physics?

Research on orthogonal Lie groups has many applications in physics. One example is in the study of quantum mechanics, where these groups are used to describe the symmetries of particles and their interactions. They are also used in the study of general relativity, where they help to understand the symmetries of spacetime. Additionally, orthogonal Lie groups have applications in condensed matter physics, nuclear physics, and other areas of physics.

## 4. How does the study of orthogonal Lie groups contribute to our understanding of the universe?

The study of orthogonal Lie groups is essential for understanding the fundamental laws of the universe. These groups provide a mathematical framework for describing symmetries and predicting the behavior of physical systems. By studying the symmetries of the universe, we can gain insights into the underlying principles that govern the behavior of matter and energy.

## 5. What are some challenges in researching orthogonal Lie groups for physics applications?

One challenge in researching orthogonal Lie groups for physics applications is the complexity of the mathematics involved. These groups are highly abstract and can be difficult to visualize, making it challenging to apply them to real-world problems. Additionally, there are still many unanswered questions about the properties and applications of these groups, which requires further research and collaboration among scientists in different fields.