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 }