PIDelta
PIDelta[i,j]
is the Kronecker-delta in the Pauli space. PIDelta[i,j]
is transformed into PauliIndexDelta[PauliIndex[i],PauliIndex[j]]
by FeynCalcInternal.
See also
Overview, PauliChain, PCHN, PauliIndex, PauliIndexDelta, PauliChainJoin, PauliChainExpand, PauliChainFactor.
Examples
δij
PIDelta[i, i]
PauliChainJoin[%]
δii
4
PIDelta[i, j]^2
PauliChainJoin[%]
δij2
4
PIDelta[i, j] PIDelta[j, k]
PauliChainJoin[%]
δijδjk
δik
ex = PIDelta[i2, i3] PIDelta[i4, i5] PCHN[i7, PauliXi[I]] PauliChain[PauliEta[-I], PauliIndex[i0]] PauliChain[PauliSigma[CartesianIndex[a]], PauliIndex[i1], PauliIndex[i2]] PauliChain[PauliSigma[CartesianIndex[b]], PauliIndex[i5], PauliIndex[i6]] PauliChain[m + PauliSigma[CartesianMomentum[p]], PauliIndex[i3], PauliIndex[i4]]
(ξ)i7(η†)i0δi2i3δi4i5(σa)i1i2(σb)i5i6(σ⋅p+m)i3i4
(ξ)i7(η†)i0(σa.(σ⋅p+m).σb)i1i6
PauliChainJoin[ex PIDelta[i0, i1]]
(ξ)i7(η†.σa.(σ⋅p+m).σb)i6
PauliChainJoin[% PIDelta[i7, i6]]
η†.σa.(σ⋅p+m).σb.ξ