FeynCalc manual (development version)

Explicit

Explicit[exp] inserts explicit expressions of GluonVertex, Twist2GluonOperator, SUNF etc. in exp.

To rewrite the SU(N)SU(N) structure constants in terms of traces, please set the corresponding options SUNF or SUND to True.

Explicit is also an option for FieldStrength, GluonVertex, SUNF, Twist2GluonOperator etc. If set to True the full form of the operator is inserted.

See also

Overview, GluonVertex, Twist2GluonOperator.

Examples

gv = GluonVertex[p, \[Mu], a, q, \[Nu], b, r, \[Rho], c]

fabcVμνρ(pqr)f^{abc} V^{\mu \nu \rho }(p\text{, }q\text{, }r)

Explicit[gv]

gsfabc(gμν(pρqρ)+gμρ(rνpν)+gνρ(qμrμ))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)

Explicit[gv, SUNF -> True]

2igs(tr(Ta.Tc.Tb)tr(Ta.Tb.Tc))(gμν(pρqρ)+gμρ(rνpν)+gνρ(qμrμ))2 i g_s \left(\text{tr}\left(T^a.T^c.T^b\right)-\text{tr}\left(T^a.T^b.T^c\right)\right) \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)

Twist2GluonOperator[p, \[Mu], a, \[Nu], b] 
 
Explicit[%]

12((1)m+1)δab(OμνG2(p))\frac{1}{2} \left((-1)^m+1\right) \delta ^{ab} \left(O_{\mu \, \nu }^{\text{G2}}(p)\right)

12((1)m+1)δab(Δp)m2(gμν(Δp)2+p2ΔμΔν(Δp)(Δνpμ+Δμpν))\frac{1}{2} \left((-1)^m+1\right) \delta ^{ab} (\Delta \cdot p)^{m-2} \left(g^{\mu \nu } (\Delta \cdot p)^2+p^2 \Delta ^{\mu } \Delta ^{\nu }-(\Delta \cdot p) \left(\Delta ^{\nu } p^{\mu }+\Delta ^{\mu } p^{\nu }\right)\right)

FieldStrength[\[Mu], \[Nu], a] 
 
Explicit[%]

FμνaF_{\mu \nu }^a

gsfab19  c20Aμb19.Aνc20+(μAνa)(νAμa)g_s f^{a\text{b19}\;\text{c20}} A_{\mu }^{\text{b19}}.A_{\nu }^{\text{c20}}+\left(\partial _{\mu }A_{\nu }^a\right)-\left(\partial _{\nu }A_{\mu }^a\right)

Explicit[SUNF[a, b, c]]

fabcf^{abc}

Explicit[SUNF[a, b, c], SUNF -> True]

2i(tr(Ta.Tc.Tb)tr(Ta.Tb.Tc))2 i \left(\text{tr}\left(T^a.T^c.T^b\right)-\text{tr}\left(T^a.T^b.T^c\right)\right)

Explicit[SUND[a, b, c]]

dabcd^{abc}

Explicit[SUND[a, b, c], SUND -> True]

2  tr(Ta.Tb.Tc)+2  tr(Tb.Ta.Tc)2 \;\text{tr}\left(T^a.T^b.T^c\right)+2 \;\text{tr}\left(T^b.T^a.T^c\right)