Explicit[exp] inserts explicit expressions of GluonVertex, Twist2GluonOperator, SUNF etc. in exp.
To rewrite the 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.
Overview, GluonVertex, Twist2GluonOperator.
gv = GluonVertex[p, \[Mu], a, q, \[Nu], b, r, \[Rho], c]f^{abc} V^{\mu \nu \rho }(p\text{, }q\text{, }r)
Explicit[gv]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]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[%]\frac{1}{2} \left((-1)^m+1\right) \delta ^{ab} \left(O_{\mu \, \nu }^{\text{G2}}(p)\right)
\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[%]F_{\mu \nu }^a
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]]f^{abc}
Explicit[SUNF[a, b, c], SUNF -> True]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]]d^{abc}
Explicit[SUND[a, b, c], SUND -> True]2 \;\text{tr}\left(T^a.T^b.T^c\right)+2 \;\text{tr}\left(T^b.T^a.T^c\right)