<< fc.m

FeynCalc 4.1.0.3b     Evaluate ?FeynCalc for help or visit www.feyncalc.org

\(Clear[t, t1, t2, t3, t4, t5, n, q, a, b, n, re1, re2]; 

    ScalarProduct[n, n] = 0; \)

The gluon propagator should be the inverse   tensor  of (D^(-1))[μ, ν] or t[μ,ν] when n^2=0.

\(t[μ_, ν_] := 
      \((MT[μ, ν] ScalarProduct[q, q] - 
FV[q, μ] FV[q, ν] + 
            \(1\/λ\) FV[n, μ] FV[n, ν])\) I\)

t[μ, ν]

t1[μ_, ν_] := 
      GluonPropagator[q, μ, a, ν, b, 
        Gauge -> {Momentum[n], λ}]

t1[μ, ν]

The correct definition of gluon propagator t2[μ,ν] when (n^2)=0.

t2[a_, b_] := 
      I (-MT[a, b] + 
              ((FV[n, a] FV[q, b] + FV[q, a] FV[n, b])/ScalarProduct)[n, 
                  q] - (1/ScalarProduct[n, q]^2)*
                (λ*ScalarProduct[q, q] FV[q, a] FV[q, b]))/
          ScalarProduct[q, q]

t2[μ, ν]

We can compare the difference of  " t1[μ,ν] "'and "t2[μ,ν]"

\(t3[μ_, ν_] := t[μ, ρ]*t1[ν, ρ]; 

    t4[μ_, ν_] := t[μ, ρ]*t2[ν, ρ]; \)

re1 = Calc[Expand[t3[μ, ν]]]

re2 = Calc[Expand[t4[μ, ν]]]

So  t1 is not the correct one, and the gluon propagator in axial gauge should be t2(when n^2=0)