GluonPropagator[p, {mu, a}, {nu, b}] or GluonPropagator[p, mu, a, nu, b] yields the gluon propagator.
GluonPropagator[p, {mu}, {nu}] or GluonPropagator[p, mu, nu] omits the SUNDelta.
GP can be used as an abbreviation of GluonPropagator.
The gauge and the dimension are determined by the options Gauge and Dimension. The following settings of Gauge are possible:
1 for the Feynman gaugealpha for the general covariant gauge{Momentum[n] ,1} for the axial gaugeOverview, GluonSelfEnergy, GluonVertex, GluonGhostVertex, GhostPropagator, GluonGhostVertex.
GluonPropagator[p, \[Mu], a, \[Nu], b]
Explicit[%]\Pi _{ab}^{\mu \nu }(p)
-\frac{i \delta ^{ab} g^{\mu \nu }}{p^2}
GP[p, \[Mu], a, \[Nu], b, Gauge -> \[Alpha]]
Explicit[%]\Pi _{ab}^{\mu \nu }(p)
\frac{i \delta ^{ab} \left(\frac{(1-\alpha ) p^{\mu } p^{\nu }}{p^2}-g^{\mu \nu }\right)}{p^2}
GluonPropagator[p, \[Mu], a, \[Nu], b, Gauge -> {Momentum[n], 1}, Explicit -> True]\frac{i \delta ^{ab} \left(\frac{p^{\mu } \overline{n}^{\nu }+p^{\nu } \overline{n}^{\mu }}{(\overline{n}\cdot \overline{p}+i \eta )}-\frac{\overline{n}^2 p^{\mu } p^{\nu }-p^2 \overline{n}^{\mu } \overline{n}^{\nu }}{(\overline{n}\cdot \overline{p}+i \eta )^{21}}-g^{\mu \nu }\right)}{p^2}
GP[p, \[Mu], \[Nu]]\Pi _g^{\mu \nu }(p)
Explicit[%]-\frac{i g^{\mu \nu }}{p^2}
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 1] // Explicit-\frac{i C_A g_s^2 S_n \delta ^{ab} \left(\frac{11 p^{\mu } p^{\nu }}{3}-\frac{19}{6} p^2 g^{\mu \nu }\right)}{\varepsilon }
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 2] // Explicit-\frac{i C_A g_s^2 S_n \delta ^{ab} \left(-\frac{1}{6} p^2 g^{\mu \nu }-\frac{1}{3} p^{\mu } p^{\nu }\right)}{\varepsilon }
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 3] // Explicit-\frac{2 i T_f g_s^2 S_n \delta ^{ab} \left(\frac{4}{3} p^2 g^{\mu \nu }-\frac{4 p^{\mu } p^{\nu }}{3}\right)}{\varepsilon }
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 4] // Explicit-\frac{i C_A g_s^2 S_n \delta ^{ab} \left(\frac{10 p^{\mu } p^{\nu }}{3}-\frac{10}{3} p^2 g^{\mu \nu }\right)}{\varepsilon }
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 5] // Explicit\frac{i C_A g_s^2 S_n \delta ^{ab} \left(\frac{10 p^{\mu } p^{\nu }}{3}-\frac{10}{3} p^2 g^{\mu \nu }\right)}{\varepsilon }+\frac{i T_f g_s^2 S_n \delta ^{ab} \left(\frac{4}{3} p^2 g^{\mu \nu }-\frac{4 p^{\mu } p^{\nu }}{3}\right)}{\varepsilon }