I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have T2=−1 rather than T2=+1, where T is the time reversal operator. I understand from the Wikipedia article that requiring that energy stay positive forces T to be represented by an anti-unitary operator. But I don't see how this forces T2=−1. (Or maybe it doesn't force it, it merely allows it?)
Here's another version of my question. There are two distinct double covers of the Lie group O(n) which restrict to the familiar Spin(n)→SO(n) cover on SO(n); they are called Pin+(n) and Pin−(n). If R∈O(n) is a reflection and ˜R∈Pin±(n) covers R, then ˜R2=±1. So saying that T2=−1 means we are in Pin− rather than Pin+. (I'm assuming Euclidean signature here.) My question (version 2): Under what circumstances are we forced to use Pin− rather than Pin+ here?
This post imported from StackExchange Physics at 2014-04-05 17:29 (UCT), posted by SE-user Kevin Walker