  In order to obtain proper wave-function renormalization constants for
unstable fermion and consist with Breit-Wigner formula in the resonant region,
We have assumed an extension of the LSZ reduction formula for unstable fermion
and adopted on-shell mass renormalization scheme in the framework of without
field renormaization. The comparison of gauge dependence of physical amplitude
between on-shell mass renormalization and complex-pole mass renormalization has
been discussed. After obtaining the fermion wave-function renormalization
constants, we extend them to two matrices in order to include the contributions
of off-diagonal two-point diagrams at fermion external legs for the convenience
of calculations of S-matrix elements.
