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.(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Rotations and reflections

**Physics Forums | Science Articles, Homework Help, Discussion**