- #1
belliott4488
- 662
- 1
What's the correct way to state the relationship between these two Lie groups? One is the "covering group" of the other, right? Okay, then - what's that mean, to a non-expert?
I know the basics, i.e. SO(3) can be represented by rotation matrices in 3-space, and U(2) does the same in a complex 2-space, but how are the two connected?
What I'd really like to know is how to explain to non-physicists (like the engineers I work with) how it is that quaternions are used to represent body orientations in 3-space and why the angles pick up a factor of 1/2. I know it's connected to the business of a 2-pi rotation in complex 2-space picking up a factor of -1 so that you have to do a rotation by 4-pi to get back to your initial orientation ... but I don't really know what that means.
Any helpful pictures or explanations?
Thanks,
Bruce
I know the basics, i.e. SO(3) can be represented by rotation matrices in 3-space, and U(2) does the same in a complex 2-space, but how are the two connected?
What I'd really like to know is how to explain to non-physicists (like the engineers I work with) how it is that quaternions are used to represent body orientations in 3-space and why the angles pick up a factor of 1/2. I know it's connected to the business of a 2-pi rotation in complex 2-space picking up a factor of -1 so that you have to do a rotation by 4-pi to get back to your initial orientation ... but I don't really know what that means.
Any helpful pictures or explanations?
Thanks,
Bruce