Spin wavefunction for 2 electrons

[dyn]

In 4-D Hilbert space for 2 electrons is |up1>|down2> equivalent to |down1>|up2> due to electrons being identical ?

 

[bhobba]

In 4-D Hilbert space for 2 electrons is |up1>|down2> equivalent to |down1>|up2> due to electrons being identical ?

Under exchange electrons, being Fermions, changes sign:
http://en.wikipedia.org/wiki/Identical_particles#Exchange_symmetry

Thanks
Bill