- #1

LukeD

- 355

- 3

The argument given in my textbook is: define an exchange operator P. "Clearly" P^2 = I. Therefore, the eigenvalues of P are +1 and -1. Systems of identical particles are eigenvectors of an exchange operator, so they are therefore either symmetric or antisymmetric under exchange of particles.

On the other hand, I don't see why we need P^2 = I. We can have P^2 = e^(i theta) for any value of theta because the only requirement we have is that exchanging twice leaves us with a state that is physically indistinguishable.

So what gives? Is the argument given in my book completely bogus? Can someone direct me to another book that has an explanation of bosons & fermions? (I'm looking at Townsend by the way)