Understandig Representation of SO(3) Group

In summary, the person is new to Group Theory and is struggling with understanding the Representation of SO(3) Groups. They ask for useful information about it and receive various resources, including a link to a Wikipedia page and some PDFs. They also recommend a textbook for studying Group Theory in the context of quantum mechanics.
  • #1
torehan
41
0
Hi, I'm very new on Group Theory, and lacking of easy to understand document on it.

I can't get Representation of SO(3) Groups.

Is there anyone can tell me useful information about it?

Thanks,
Tore Han
 
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  • #2
SO(3) is ONE group.. not groups.

Here you have some basic info about SO(3) (rotations)
http://en.wikipedia.org/wiki/SO(3 [Broken])

I can give you this link, but there is not some much about matrix lie groups in it, but I found it very useful for learning basics of groups at least.
http://www.teorfys.uu.se/people/minahan/Courses/Mathmeth/notes.pdf [Broken]

I have not used this source so much yet, but it looks quite good:
http://www.math.duke.edu/~bryant/ParkCityLectures.pdf

If you want to study group theory for quantum mechanics such as angular mometa etc, I recommend "Modern Quantum Mechanics" by sakurai, chapter 3 and 4
 
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  • #3
Sorry about my mistake.

And thanks for the informations. it will be useful.
 

1. What is the SO(3) group?

The SO(3) group, also known as the special orthogonal group in three dimensions, is a mathematical concept used to describe rotations in three-dimensional space. It consists of all possible rotations around a fixed point that preserve the orientation of an object.

2. How is the SO(3) group represented?

The SO(3) group is typically represented using a 3x3 matrix, known as a rotation matrix. This matrix contains the nine elements that describe the rotation and can be used to perform the rotation on a three-dimensional object.

3. What is the significance of the SO(3) group in physics?

The SO(3) group is significant in physics because it is used to describe the symmetries of physical systems. Many physical laws and equations are invariant under rotations, and the SO(3) group helps to understand and apply these symmetries.

4. How is the SO(3) group related to other mathematical concepts?

The SO(3) group is closely related to other mathematical concepts, such as the special unitary group SU(2) and the rotation group in four dimensions SO(4). These groups are all examples of Lie groups, which are used to study continuous symmetries in mathematics and physics.

5. How is the SO(3) group used in computer graphics?

In computer graphics, the SO(3) group is used to rotate and orient objects in three-dimensional space. It is used in 3D modeling, animation, and video game development to create realistic movements and transformations of objects. The rotation matrices of the SO(3) group are also used in algorithms for 3D rendering and image processing.

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