Fermion field renormalization prescriptions

We discuss all possible fermion field renormalization prescriptions in conventional field renormalization meaning and mainly pay attention to the imaginary part of unstable fermion Field Renormalization Constants (FRC). We find that introducing the off-diagonal fermion FRC leads to the decay widths of physical processes $t\to c Z$ and $b\to s \gamma$ gauge-parameter dependent. We also discuss the necessity of renormalizing the bare fields in conventional quantum field theory.