I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must either be symmetric with respect to the exchange operator, or antisymmetric.
Why can we not have some states that are symmetric with respect to the exchange operator, and some that are antisymmetric? As far as I can tell, this question is not even referenced anywhere in the material I've been reading.
I understand that this is the symmetrization postulate, but is there any chance anyone could elucidate on why this is the case? Is this a consequence of quantum field theory?