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.
Overview, GluonPropagator, GluonGhostVertex.
GluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}]
Explicit[%]f^{abc} V^{\mu \nu \rho }(p\text{, }q\text{, }r)
g_s f^{abc} \left(g^{\mu \nu } \left(p^{\rho }-q^{\rho }\right)+g^{\mu \rho } \left(r^{\nu }-p^{\nu }\right)+g^{\nu \rho } \left(q^{\mu }-r^{\mu }\right)\right)
GV[{p, \[Mu]}, {q, \[Nu]}, {r, \[Rho]}]
Explicit[%]V^{\mu \nu \rho }(p\text{, }q\text{, }r)
g_s \left(g^{\mu \nu } \left(p^{\rho }-q^{\rho }\right)+g^{\mu \rho } \left(r^{\nu }-p^{\nu }\right)+g^{\nu \rho } \left(q^{\mu }-r^{\mu }\right)\right)
GluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {r, \[Rho], c}, {s, \[Sigma], d}]
Explicit[%]V_{abcd}^{\mu \nu \rho \sigma }(p\text{, }q\text{, }r\text{, }s)
-i g_s^2 \left(f^{ad\text{FCGV}(\text{u19})} f^{bc\text{FCGV}(\text{u19})} \left(g^{\mu \nu } g^{\rho \sigma }-g^{\mu \rho } g^{\nu \sigma }\right)+f^{ac\text{FCGV}(\text{u19})} f^{bd\text{FCGV}(\text{u19})} \left(g^{\mu \nu } g^{\rho \sigma }-g^{\mu \sigma } g^{\nu \rho }\right)+f^{ab\text{FCGV}(\text{u19})} f^{cd\text{FCGV}(\text{u19})} \left(g^{\mu \rho } g^{\nu \sigma }-g^{\mu \sigma } g^{\nu \rho }\right)\right)
GV[{\[Mu], a}, {\[Nu], b}, {\[Rho], c}, {\[Sigma], d}]
Explicit[%]V^{abcd}
-i g_s^2 \left(f^{ad\text{FCGV}(\text{u20})} f^{bc\text{FCGV}(\text{u20})} \left(g^{\mu \nu } g^{\rho \sigma }-g^{\mu \rho } g^{\nu \sigma }\right)+f^{ac\text{FCGV}(\text{u20})} f^{bd\text{FCGV}(\text{u20})} \left(g^{\mu \nu } g^{\rho \sigma }-g^{\mu \sigma } g^{\nu \rho }\right)+f^{ab\text{FCGV}(\text{u20})} f^{cd\text{FCGV}(\text{u20})} \left(g^{\mu \rho } g^{\nu \sigma }-g^{\mu \sigma } g^{\nu \rho }\right)\right)