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)