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In order to obtain proper wave-function renormalization constants forunstable fermion and consist with Breit-Wigner formula in the resonant region,We have assumed an extension of the LSZ reduction formula for unstable fermionand adopted on-shell mass renormalization scheme in the framework of withoutfield renormaization. The comparison of gauge dependence of physical amplitudebetween on-shell mass renormalization and complex-pole mass renormalization hasbeen discussed. After obtaining the fermion wave-function renormalizationconstants, we extend them to two matrices in order to include the contributionsof off-diagonal two-point diagrams at fermion external legs for the convenienceof calculations of S-matrix elements.Comment: 11 pages, 2 figure

A new renormalization scheme for the fermion field in the standard model