Pauli Exclusion Principle

Cannot have two identical fermions in the same state.

So if we have \(|\Psi_1\rangle = |ab\rangle\) and \(|\Psi_2\rangle = |ba\rangle\). Then for identical bosons, we have \(|\Psi_S\rangle = \frac{1}{\sqrt{2}}\left(|\Psi_1\rangle + |\Psi_2\rangle\right)\). Then for identical fermions, we have \(|\Psi_A\rangle = \frac{1}{\sqrt{2}}\left(|\Psi_1\rangle - |\Psi_2\rangle\right)\).

So if \(a=b\) then the fermionic wavefunction is zero.