  Adiabatic dynamics of conduction electrons in antiferromagnetic (AFM)
materials with slowly varying spin texture is developed. Quite different from
the ferromagnetic (FM) case, adiabaticity in AFM texture does not imply perfect
alignment of conduction electron spins with background profile, instead, it
introduces an internal dynamics between degenerate bands. As a result, the
orbital motion of conduction electrons becomes spin-dependent and is affected
by two emergent gauge fields: one of them is the non-Abelian version of what
has been discovered in FM systems; the other leads to an anomalous velocity
that has no FM counterpart. Two examples with experimental predictions are
provided.
