FCColorIsolate
FCColorIsolate[exp]
wraps colored objects (SUNT
, SUNF
etc.) into heads specified by the user.
See also
Overview, SUNT, SUNF.
Examples
FCColorIsolate
provides an easy way to extract the color structures present in the expression (e.g. an amplitude)
amp = (Spinor[Momentum[p2], SMP["m_u"], 1] . (-I GA[\[Mu]] SMP["g_s"] SUNTF[{Glu2},
Col3, Col5]) . (GS[-k1 + p2] + SMP["m_u"]) . (-I GA[\[Nu]] SMP["g_s"] SUNTF[{Glu4},
Col5, Col1]) . Spinor[Momentum[p1], SMP["m_u"], 1] FAD[{k1 - p2,
SMP["m_u"]}, Dimension -> 4] FV[Polarization[k1, I], \[Mu]] FV[Polarization[k2,
-I], \[Nu]] + Spinor[Momentum[p2], SMP["m_u"], 1] . (-I GA[\[Nu]] SMP["g_s"] SUNTF[{Glu4},
Col3, Col5]) . (GS[k2 + p2] + SMP["m_u"]) . (-I GA[\[Mu]] SMP["g_s"] SUNTF[{Glu2},
Col5, Col1]) . Spinor[Momentum[p1], SMP["m_u"], 1] FAD[{-k2 - p2, SMP["m_u"]},
Dimension -> 4] FV[Polarization[k1, I], \[Mu]] FV[Polarization[k2, -I],
\[Nu]] - Spinor[Momentum[p2], SMP["m_u"], 1] . (-I GA[Lor3] SMP["g_s"] SUNTF[{Glu5},
Col3, Col1]) . Spinor[Momentum[p1], SMP["m_u"], 1] FAD[-k1 + k2,
Dimension -> 4] FV[Polarization[k1, I], \[Mu]] FV[Polarization[k2, -I], \[Nu]] MT[Lor3,
Lor4] (FV[2 k1 - k2, \[Nu]] MT[Lor4, \[Mu]] + FV[-k1 + 2 k2, \[Mu]] MT[Lor4, \[Nu]] + FV[-k1 - k2,
Lor4] MT[\[Mu], \[Nu]]) SMP["g_s"] SUNF[Glu2, Glu4, Glu5])
(k1−p2)2−mu2εˉμ(k1)εˉ∗ν(k2)(φ(p2,mu)).(−igsγˉμTCol3Col5Glu2).(γˉ⋅(p2−k1)+mu).(−igsγˉνTCol5Col1Glu4).(φ(p1,mu))+(−k2−p2)2−mu2εˉμ(k1)εˉ∗ν(k2)(φ(p2,mu)).(−igsγˉνTCol3Col5Glu4).(γˉ⋅(k2+p2)+mu).(−igsγˉμTCol5Col1Glu2).(φ(p1,mu))−(k2−k1)21gsgˉLor3Lor4εˉμ(k1)εˉ∗ν(k2)fGlu2Glu4Glu5(gˉLor4μ(2k1−k2)ν+gˉLor4ν(2k2−k1)μ+gˉμν(−k1−k2)Lor4)(φ(p2,mu)).(−igsγˉLor3TCol3Col1Glu5).(φ(p1,mu))
ampIso = FCColorIsolate[amp, Head -> colorS]
−(k1−p2)2−mu2gs2εˉμ(k1)εˉ∗ν(k2)colorS(TCol5Col1Glu4TCol3Col5Glu2)(φ(p2,mu)).γˉμ.(γˉ⋅(p2−k1)+mu).γˉν.(φ(p1,mu))−(−k2−p2)2−mu2gs2εˉμ(k1)εˉ∗ν(k2)colorS(TCol5Col1Glu2TCol3Col5Glu4)(φ(p2,mu)).γˉν.(γˉ⋅(k2+p2)+mu).γˉμ.(φ(p1,mu))+(k2−k1)21igs2gˉLor3Lor4εˉμ(k1)εˉ∗ν(k2)(gˉμν(−k1−k2)Lor4+gˉLor4ν(2k2−k1)μ+gˉLor4μ(2k1−k2)ν)colorS(TCol3Col1Glu5fGlu2Glu4Glu5)(φ(p2,mu)).γˉLor3.(φ(p1,mu))
Now that all color structures are wrapped into the head colorS
it is easy to extract them to a separate list
{colorS(TCol5Col1Glu2TCol3Col5Glu4),colorS(TCol5Col1Glu4TCol3Col5Glu2),colorS(TCol3Col1Glu5fGlu2Glu4Glu5)}
This way we obtain a sorted list of all unique color structures in amp
.
ClearAll[amp, ampIso, colorS]