- #1
Bobhawke
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In R^2, a reflection can be achieved equally well by a rotation, because the group space of U(1) is connected. Visually I think of this as being able to peform a rotation that moves the positive y-axis into the negative y-axis and vice versa and without changing the x-axis by imagining R^2 as embedded in R^3 and rotating about the x axis, so it is unchanged but the y-axis sweeps through the extra dimension and eventually gets turned upside down.
In R^3, rotations and reflections are not connected. My question is, at what point does the analogue of the above reasoning fail for R^3, and also does the dis-connectedness of the group space have anything to do with the fact that the group is now non-abelian?
Thanks
In R^3, rotations and reflections are not connected. My question is, at what point does the analogue of the above reasoning fail for R^3, and also does the dis-connectedness of the group space have anything to do with the fact that the group is now non-abelian?
Thanks