  With a non-unitary transformation, the Lagrangian of a Dirac fermion is
decomposed into two decoupled sectors. We propose to describe massive
relativistic fermions in gauge theories in a two-component form. All relations
between the Green's functions in this form and those in the conventional
four-component form are derived. It is shown that the S-matrix elements in both
forms are exactly the same. The description of the fermion in the new form
simplifies significantly the gamma-matrix algebra in the four-component form.
In particular, in perturbative calculations the propagator of the fermion is a
scalar function. The advantages of the two-component form make it very useful
in practical applications.
