BackgroundGluonVertex
BackgroundGluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}]
yields the 3-gluon vertex in the background field gauge, where the first set of arguments corresponds to the external background field. BackgroundGluonVertex[{p, mu, a}, {q, nu, b}, {k, la, c}, {s, si, d}]
yields the 4-gluon vertex, with {p, mu ,a}
and {k, la, c}
denoting the external background fields.
The gauge, dimension and the name of the coupling constant are determined by the options Gauge
, Dimension
and CouplingConstant
.
The Feynman rules are taken from L. Abbot NPB 185 (1981), 189-203; except that all momenta are incoming. Note that Abbot’s coupling constant convention is consistent with the default setting of GluonVertex
.
See also
Overview
Examples
BackgroundGluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Lambda], c}]
gsfabc(gμν(−k+p−q)λ+gλμ(k−p+q)ν+gλν(q−k)μ)
BackgroundGluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Lambda], c}, {s, \[Sigma], d}]
−igs2(fadFCGV(u19)fbcFCGV(u19)(gλσgμν−gλνgμσ−gλμgνσ)+facFCGV(u19)fbdFCGV(u19)(gλσgμν−gλνgμσ)+fabFCGV(u19)fcdFCGV(u19)(gλσgμν−gλνgμσ+gλμgνσ))
BackgroundGluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Lambda], c},Gauge -> \[Alpha]]
gsfabc(gμν(−αk+p−q)λ+gλμ(k−p+αq)ν+gλν(q−k)μ)
BackgroundGluonVertex[{p, \[Mu], a}, {q, \[Nu], b}, {k, \[Lambda], c}, {s, \[Sigma], d}, Gauge -> \[Alpha]]
−igs2(fadFCGV(u20)fbcFCGV(u20)(−αgλνgμσ+gλσgμν−gλμgνσ)+fabFCGV(u20)fcdFCGV(u20)(αgλσgμν−gλνgμσ+gλμgνσ)+facFCGV(u20)fbdFCGV(u20)(gλσgμν−gλνgμσ))