Talk:Exchange operator

Sorry about the edit summary...
For, the link should be talk:anyon not talk:exchange operator. This is the second time an edit summary has gone wrong this morning... M&and;Ŝc2ħεИτlk 07:40, 18 August 2013 (UTC)

Indistinguishability
The logic when applying the exchange operator twice is not sound. Why should the state after two exchanges be the same? It could acquire any phase and still be indistinguishable from the original state. This is the case, e.g. when, a spin-1/2 particle is rotated twice by 180 degrees. That should be indistinguishable from virtually rotating the coordinate system, and yet, the state acquire a phase of exp(i pi)=-1. The difference is that for indistinguishable particles it is impossible to the distinguish the reverse operation P^-1 from P itself. Therefore P^2|x1,x2>=P^{-1}P|x1,x2>=|x1,x2>. For a 180 degree rotation of a spin-1/2 that is not the case as it can be done, e.g., by putting the spin into a magnetic field and rotating it adiabatically. But in this case, the forward rotation can be distinguished from the backward rotation, because the magnetic field has an orientation, which can be distinguished by comparing the spin-up and spin-down states in this field. 146.200.139.29 (talk) 20:02, 20 November 2020 (UTC)