PauliChain[x, i, j] denotes a chain of Pauli matrices x, where the Pauli indices i and j are explicit.
Overview, PCHN, PauliIndex, PauliIndexDelta, PauliChainJoin, PauliChainExpand, PauliChainFactor.
A standalone Pauli matrix \sigma^i_{jk}
PauliChain[PauliSigma[CartesianIndex[a]], PauliIndex[i], PauliIndex[j]]\left(\overline{\sigma }^a\right){}_{ij}
A chain of Pauli matrices with open indices
PauliChain[PauliSigma[CartesianIndex[a, D - 1], D - 1] . PauliSigma[CartesianIndex[b, D - 1], D - 1], PauliIndex[i], PauliIndex[j]]\left(\sigma ^a.\sigma ^b\right){}_{ij}
A PauliChain with only two arguments denotes a spinor component
PauliChain[PauliXi[-I], PauliIndex[i]]\left(\xi ^{\dagger }\right){}_i
PauliChain[PauliEta[-I], PauliIndex[i]]\left(\eta ^{\dagger }\right){}_i
PauliChain[PauliIndex[i], PauliXi[I]](\xi )_i
PauliChain[PauliIndex[i], PauliEta[I]](\eta )_i
The chain may also be partially open or closed
PauliChain[PauliSigma[CartesianIndex[a]] . (m + PauliSigma[CartesianMomentum[p]]) . PauliSigma[CartesianIndex[b]], PauliXi[-I], PauliIndex[j]]\left(\xi ^{\dagger }.\overline{\sigma }^a.\left(\overline{\sigma }\cdot \overline{p}+m\right).\overline{\sigma }^b\right){}_j
PauliChain[PauliSigma[CartesianIndex[a]] . (m + PauliSigma[CartesianMomentum[p]]) . PauliSigma[CartesianIndex[b]], PauliIndex[i], PauliXi[I]]\left(\overline{\sigma }^a.\left(\overline{\sigma }\cdot \overline{p}+m\right).\overline{\sigma }^b.\xi \right){}_i
PauliChain[PauliSigma[CartesianIndex[a]] . (m + PauliSigma[CartesianMomentum[p]]) . PauliSigma[CartesianIndex[b]], PauliXi[-I], PauliEta[I]]\left(\xi ^{\dagger }.\overline{\sigma }^a.\left(\overline{\sigma }\cdot \overline{p}+m\right).\overline{\sigma }^b.\eta \right)
PauliChain[1, PauliXi[-I], PauliEta[I]]\left(\xi ^{\dagger }.\eta \right)