FeynCalc manual (development version)

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])

εˉμ(k1)εˉν(k2)(φ(p2,mu)).(igsγˉμTCol3  Col5Glu2).(γˉ(p2k1)+mu).(igsγˉνTCol5  Col1Glu4).(φ(p1,mu))(k1p2)2mu2+εˉμ(k1)εˉν(k2)(φ(p2,mu)).(igsγˉνTCol3  Col5Glu4).(γˉ(k2+p2)+mu).(igsγˉμTCol5  Col1Glu2).(φ(p1,mu))(k2p2)2mu21(k2k1)2gsgˉLor3  Lor4εˉμ(k1)εˉν(k2)fGlu2  Glu4  Glu5(gˉLor4μ(2k1k2)ν+gˉLor4ν(2k2k1)μ+gˉμν(k1k2)Lor4)(φ(p2,mu)).(igsγˉLor3TCol3  Col1Glu5).(φ(p1,mu))\frac{\bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) \left(\varphi (\overline{\text{p2}},m_u)\right).\left(-i g_s \bar{\gamma }^{\mu } T_{\text{Col3}\;\text{Col5}}^{\text{Glu2}}\right).\left(\bar{\gamma }\cdot \left(\overline{\text{p2}}-\overline{\text{k1}}\right)+m_u\right).\left(-i g_s \bar{\gamma }^{\nu } T_{\text{Col5}\;\text{Col1}}^{\text{Glu4}}\right).\left(\varphi (\overline{\text{p1}},m_u)\right)}{(\overline{\text{k1}}-\overline{\text{p2}})^2-m_u^2}+\frac{\bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) \left(\varphi (\overline{\text{p2}},m_u)\right).\left(-i g_s \bar{\gamma }^{\nu } T_{\text{Col3}\;\text{Col5}}^{\text{Glu4}}\right).\left(\bar{\gamma }\cdot \left(\overline{\text{k2}}+\overline{\text{p2}}\right)+m_u\right).\left(-i g_s \bar{\gamma }^{\mu } T_{\text{Col5}\;\text{Col1}}^{\text{Glu2}}\right).\left(\varphi (\overline{\text{p1}},m_u)\right)}{(-\overline{\text{k2}}-\overline{\text{p2}})^2-m_u^2}-\frac{1}{(\overline{\text{k2}}-\overline{\text{k1}})^2}g_s \bar{g}^{\text{Lor3}\;\text{Lor4}} \bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) f^{\text{Glu2}\;\text{Glu4}\;\text{Glu5}} \left(\bar{g}^{\text{Lor4}\mu } \left(2 \overline{\text{k1}}-\overline{\text{k2}}\right)^{\nu }+\bar{g}^{\text{Lor4}\nu } \left(2 \overline{\text{k2}}-\overline{\text{k1}}\right)^{\mu }+\bar{g}^{\mu \nu } \left(-\overline{\text{k1}}-\overline{\text{k2}}\right)^{\text{Lor4}}\right) \left(\varphi (\overline{\text{p2}},m_u)\right).\left(-i g_s \bar{\gamma }^{\text{Lor3}} T_{\text{Col3}\;\text{Col1}}^{\text{Glu5}}\right).\left(\varphi (\overline{\text{p1}},m_u)\right)

ampIso = FCColorIsolate[amp, Head -> colorS]

gs2εˉμ(k1)εˉν(k2)  colorS(TCol5  Col1Glu4TCol3  Col5Glu2)(φ(p2,mu)).γˉμ.(γˉ(p2k1)+mu).γˉν.(φ(p1,mu))(k1p2)2mu2gs2εˉμ(k1)εˉν(k2)  colorS(TCol5  Col1Glu2TCol3  Col5Glu4)(φ(p2,mu)).γˉν.(γˉ(k2+p2)+mu).γˉμ.(φ(p1,mu))(k2p2)2mu2+1(k2k1)2igs2gˉLor3  Lor4εˉμ(k1)εˉν(k2)(gˉμν(k1k2)Lor4+gˉLor4ν(2k2k1)μ+gˉLor4μ(2k1k2)ν)  colorS(TCol3  Col1Glu5fGlu2  Glu4  Glu5)(φ(p2,mu)).γˉLor3.(φ(p1,mu))-\frac{g_s^2 \bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) \;\text{colorS}\left(T_{\text{Col5}\;\text{Col1}}^{\text{Glu4}} T_{\text{Col3}\;\text{Col5}}^{\text{Glu2}}\right) \left(\varphi (\overline{\text{p2}},m_u)\right).\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \left(\overline{\text{p2}}-\overline{\text{k1}}\right)+m_u\right).\bar{\gamma }^{\nu }.\left(\varphi (\overline{\text{p1}},m_u)\right)}{(\overline{\text{k1}}-\overline{\text{p2}})^2-m_u^2}-\frac{g_s^2 \bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) \;\text{colorS}\left(T_{\text{Col5}\;\text{Col1}}^{\text{Glu2}} T_{\text{Col3}\;\text{Col5}}^{\text{Glu4}}\right) \left(\varphi (\overline{\text{p2}},m_u)\right).\bar{\gamma }^{\nu }.\left(\bar{\gamma }\cdot \left(\overline{\text{k2}}+\overline{\text{p2}}\right)+m_u\right).\bar{\gamma }^{\mu }.\left(\varphi (\overline{\text{p1}},m_u)\right)}{(-\overline{\text{k2}}-\overline{\text{p2}})^2-m_u^2}+\frac{1}{(\overline{\text{k2}}-\overline{\text{k1}})^2}i g_s^2 \bar{g}^{\text{Lor3}\;\text{Lor4}} \bar{\varepsilon }^{\mu }(\text{k1}) \bar{\varepsilon }^{*\nu }(\text{k2}) \left(\bar{g}^{\mu \nu } \left(-\overline{\text{k1}}-\overline{\text{k2}}\right)^{\text{Lor4}}+\bar{g}^{\text{Lor4}\nu } \left(2 \overline{\text{k2}}-\overline{\text{k1}}\right)^{\mu }+\bar{g}^{\text{Lor4}\mu } \left(2 \overline{\text{k1}}-\overline{\text{k2}}\right)^{\nu }\right) \;\text{colorS}\left(T_{\text{Col3}\;\text{Col1}}^{\text{Glu5}} f^{\text{Glu2}\;\text{Glu4}\;\text{Glu5}}\right) \left(\varphi (\overline{\text{p2}},m_u)\right).\bar{\gamma }^{\text{Lor3}}.\left(\varphi (\overline{\text{p1}},m_u)\right)

Now that all color structures are wrapped into the head colorS it is easy to extract them to a separate list

Cases2[ampIso, colorS]

{colorS(TCol5  Col1Glu2TCol3  Col5Glu4),colorS(TCol5  Col1Glu4TCol3  Col5Glu2),colorS(TCol3  Col1Glu5fGlu2  Glu4  Glu5)}\left\{\text{colorS}\left(T_{\text{Col5}\;\text{Col1}}^{\text{Glu2}} T_{\text{Col3}\;\text{Col5}}^{\text{Glu4}}\right),\text{colorS}\left(T_{\text{Col5}\;\text{Col1}}^{\text{Glu4}} T_{\text{Col3}\;\text{Col5}}^{\text{Glu2}}\right),\text{colorS}\left(T_{\text{Col3}\;\text{Col1}}^{\text{Glu5}} f^{\text{Glu2}\;\text{Glu4}\;\text{Glu5}}\right)\right\}

This way we obtain a sorted list of all unique color structures in amp.

ClearAll[amp, ampIso, colorS]