Non-Abelian holonomy of BCS and SDW quasiparticles

In this work we investigate properties of fermions in the SO(5) theory of h igh T-c superconductivity. We show that the adiabatic rime evolution of a S O(5) superspin vector leads to a non-Abelian SU(2) holonomy of the SO(5) sp inor states. Physically, this non-trivial holonomy arises From the non-zero overlap between the SDW and BCS quasiparticle stales. While the usual Berr y's phase of a SO(3) spinor is described by a Dirac magnetic monopole at th r degeneracy point, the non-Abelian holonomy of a SO(5) spinor is described by a Yang monopole at the degeneracy point and is deeply related to the ex istence of the second Hopf map from S-7 to S-4. We conclude this work by ex tending the bosonic SO(5) nonlinear sigma model to include the fermionic st ates around the gap nodes as 4 component Dirac fermions coupled to SU(2) ga uge fields in 2 + 1 dimensions. (C) 1999 Academic Press.