  We study the fermion propagator in a spatially varying classical background
field, and show that, contrary to common wisdom, it may get nontrivial gradient
corrections already at the first order in derivative expansion. This occurs
whenever the fermion self-energy acquires a spatially (or temporally) varying
pseudoscalar term, a simple example of which is given by a complex mass term
m(x)= m_R + i gamma_5 m_I. Such effective mass terms arise for example in
extensions of the Standard Model during the electroweak transition, and they
are crucial in providing the CP-violation necessary for electroweak
baryogenesis.
