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)