GluonVertex
GluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}]
or GluonVertex[p, mu, a, q, nu, b, k, la, c]
yields the 3-gluon vertex.
GluonVertex[{p, mu}, {q, nu}, {k, la}]
yields the 3-gluon vertex without color structure and the coupling constant.
GluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}, {s, si, d}]
or GluonVertex[{mu, a}, {nu, b}, {la, c}, {si, d}]
or GluonVertex[p, mu, a, q, nu, b, k, la, c , s, si, d]
or GluonVertex[mu, a, nu, b, la, c, si, d]
yields the 4-gluon vertex.
GV
can be used as an abbreviation of GluonVertex
.
The dimension and the name of the coupling constant are determined by the options Dimension
and CouplingConstant
. All momenta are flowing into the vertex.
See also
Overview, GluonPropagator, GluonGhostVertex.
Examples
GluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}]
Explicit[%]
fabcVμνρ(p, q, r)
gsfabc(gμν(pρ−qρ)+gμρ(rν−pν)+gνρ(qμ−rμ))
GV[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}]
Explicit[%]
Vμνρ(p, q, r)
gs(gμν(pρ−qρ)+gμρ(rν−pν)+gνρ(qμ−rμ))
GluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}, {s, \[Sigma], d}]
Explicit[%]
Vabcdμνρσ(p, q, r, s)
−igs2(fadFCGV(u19)fbcFCGV(u19)(gμνgρσ−gμρgνσ)+facFCGV(u19)fbdFCGV(u19)(gμνgρσ−gμσgνρ)+fabFCGV(u19)fcdFCGV(u19)(gμρgνσ−gμσgνρ))
GV[{\[Mu], a}, {\[Nu], b}, {\[Rho], c}, {\[Sigma], d}]
Explicit[%]
Vabcd
−igs2(fadFCGV(u20)fbcFCGV(u20)(gμνgρσ−gμρgνσ)+facFCGV(u20)fbdFCGV(u20)(gμνgρσ−gμσgνρ)+fabFCGV(u20)fcdFCGV(u20)(gμρgνσ−gμσgνρ))