= Solution
{c}
The non-Abelian counterpart of the photon <Ward identity> is a <Slavnov-Taylor identity>, derived from <BRST symmetry>. A <scattering amplitude> with all other external states physical vanishes when one external massless <gauge boson> <polarization vector> is replaced by its <four-momentum>. An amputated tensor with the remaining indices open need not be transverse: part <3/d> gives its explicit nonzero longitudinal remainder.
Consequently, amplitudes involving several unphysical covariant <polarization vectors> need not vanish. For example, contracting the result of part <3/d> with a timelike vector $n_\mu$ gives $ig^2\epsilon^{abc}(J_c\cdot k_2)(n\cdot k_1)/s$, nonzero in the explicit configuration there for $n=(1,0,0,0)$. Even with other states physical, the pure-gauge vector $k$ is the relevant null combination; separate timelike and spatial longitudinal basis vectors are not themselves pure gauge, and their separate amplitudes need not be zero.
These auxiliary components do \b[not] define separately observable positive probabilities. Physical states are classes in <BRST cohomology>, and the <S-matrix> preserves that physical state space in this anomaly-free <vectorlike gauge spectrum>. There is no physical transition from a physical state to a nonphysical state. The incorrect stronger statement would be that every covariant component called “unphysical” has a zero matrix element.
For <loop Feynman diagrams> or <unitarity cuts>, summing covariant gauge indices with $-g_{\mu\nu}$ propagates those auxiliary components. In a <Non-Abelian gauge theory>, their cancellation requires the interacting <Faddeev-Popov ghost fields> as well as the <gauge boson> diagrams. Ghost contributions carry their <Grassmann field> loop signs and restore the <Slavnov-Taylor identities> and physical <unitarity>. One may instead use a formulation with only physical propagating <polarization vectors>, but one cannot simply discard the ghost diagrams while retaining the <Feynman gauge> rules from part <3/a>.
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