# Fermi statistics and Berry phase

When the positions of two fermions are exchanged adiabatically in three-dimensional space, we know that the wave function gains a factor of $-1$. Is this related to Berry's phase?

• Good question. I found this paper by Berry which connects the phase change under particle exchange to the spin of the particles. – Vijay Murthy May 6 '12 at 7:19

Under these conditions, the phase acquired by the wavefunction through a 360 degrees rotation is $-1$. By the spin statistics theorem, the particle must be quantized as a fermion, even though its dynamics is described by bosonic coordinates.