GluonPropagator
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 gauge
alpha
for the general covariant gauge
{Momentum[n] ,1}
for the axial gauge
See also
Overview, GluonSelfEnergy, GluonVertex, GluonGhostVertex, GhostPropagator, GluonGhostVertex.
Examples
GluonPropagator[p, \[Mu], a, \[Nu], b]
Explicit[%]
Πabμν(p)
−p2iδabgμν
GP[p, \[Mu], a, \[Nu], b, Gauge -> \[Alpha]]
Explicit[%]
Πabμν(p)
p2iδab(p2(1−α)pμpν−gμν)
GluonPropagator[p, \[Mu], a, \[Nu], b, Gauge -> {Momentum[n], 1}, Explicit -> True]
p2iδab((n⋅p+iη)pμnν+pνnμ−(n⋅p+iη)21n2pμpν−p2nμnν−gμν)
Πgμν(p)
−p2igμν
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 1] // Explicit
−εiCAgs2Snδab(311pμpν−619p2gμν)
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 2] // Explicit
−εiCAgs2Snδab(−61p2gμν−31pμpν)
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 3] // Explicit
−ε2iTfgs2Snδab(34p2gμν−34pμpν)
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 4] // Explicit
−εiCAgs2Snδab(310pμpν−310p2gμν)
GluonPropagator[p, \[Mu], a, \[Nu], b, CounterTerm -> 5] // Explicit
εiCAgs2Snδab(310pμpν−310p2gμν)+εiTfgs2Snδab(34p2gμν−34pμpν)