  For a massive gauge theory with Higgs mechanism in a physical gauge, the
longitudinal polarization of gauge bosons can be naturally identified as
mixture of the goldstone component and a remnant gauge component that vanishes
at the limit of zero mass, making the goldstone equivalence manifest. In light
of this observation, we re-examine the Feynman rules of massive gauge theory by
treating gauge fields and their corresponding goldstone fields as single
objects, writing them uniformly as 5-component "vector" fields. The gauge group
is taken to be $SU(2)_L$ to preserve custodial symmetry. We find the derivation
of gauge-goldstone propagators becomes rather trivial by noticing there is a
remarkable parallel between massless gauge theory and massive gauge theory in
this notation. We also derive the Feynman rules of all vertices, finding the
vertex for self-interactions of vector (gauge-goldstone) bosons are especially
simplified. We then demonstrate that the new form of the longitudinal
polarization vector and the standard form give the same results for all the
3-point on-shell amplitudes. This on-shell matching confirms similar results
obtained with on-shell approach for massive scattering amplitudes by
Arkani-Hamed et.al. Finally we calculate some $1\rightarrow 2$ collinear
splitting amplitudes by making use of the new Feynman rules and the on-shell
match condition.
