DiracChain[x, i, j] denotes a chain of Dirac matrices x, where the Dirac indices i and j are explicit.
Overview, DiracChain, DCHN, DiracIndex, DiracIndexDelta, DiracChainJoin, DiracChainExpand, DiracChainFactor.
A standalone Dirac matrix
DiracChain[DiracGamma[LorentzIndex[\[Mu]]], DiracIndex[i], DiracIndex[j]]\left(\bar{\gamma }^{\mu }\right){}_{ij}
A chain of Dirac matrices with open indices
DiracChain[DiracGamma[LorentzIndex[\[Mu], D], D] . DiracGamma[LorentzIndex[\[Nu], D], D], DiracIndex[i], DiracIndex[j]]\left(\gamma ^{\mu }.\gamma ^{\nu }\right){}_{ij}
A DiracChain with only two arguments denotes a spinor component
DiracChain[Spinor[Momentum[p], m], DiracIndex[i]]\left(\varphi (\overline{p},m)\right)_i
DiracChain[Spinor[Momentum[-p], m], DiracIndex[i]]\left(\varphi (-\overline{p},m)\right)_i
DiracChain[DiracIndex[i], Spinor[Momentum[p], m]]\left(\varphi (\overline{p},m)\right)_i
DiracChain[DiracIndex[i], Spinor[Momentum[-p], m]]\left(\varphi (-\overline{p},m)\right)_i
The chain may also be partially open or closed
DiracChain[DiracGamma[LorentzIndex[\[Mu]]] . (m + DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[\[Nu]]], Spinor[Momentum[p], m, 1], DiracIndex[j]]\left(\varphi (\overline{p},m).\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }\right){}_j
DiracChain[DiracGamma[LorentzIndex[\[Mu]]] . (m + DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[\[Nu]]], DiracIndex[i], Spinor[Momentum[p], m, 1]]\left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }.\varphi (\overline{p},m)\right){}_i
DiracChain[DiracGamma[LorentzIndex[\[Mu]]] . (m + DiracGamma[Momentum[p]]) . DiracGamma[LorentzIndex[\[Nu]]], Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m2, 1]]\left(\varphi (\overline{\text{p1}},\text{m1}).\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }.\varphi (\overline{\text{p2}},\text{m2})\right)
DiracChain[1, Spinor[Momentum[p1], m1, 1], Spinor[Momentum[p2], m2, 1]]\left(\varphi (\overline{\text{p1}},\text{m1}).\varphi (\overline{\text{p2}},\text{m2})\right)