PauliIndexDelta
PauliIndexDelta[PauliIndex[i], PauliIndex[j]]
is the Kronecker-delta in the Pauli space with two explicit Pauli indices i
and j
.
See also
Overview, PauliChain, PCHN, PauliIndex, DIDelta, PauliChainJoin, PauliChainCombine, PauliChainExpand, PauliChainFactor.
Examples
PauliIndexDelta[PauliIndex[i], PauliIndex[j]]
δij
PauliIndexDelta[PauliIndex[i], PauliIndex[j]]^2
PauliChainJoin[%]
PauliChainJoin[%%, TraceOfOne -> D]
δij2
4
D
PauliIndexDelta[PauliIndex[i], PauliIndex[j]] PauliIndexDelta[PauliIndex[j], PauliIndex[k]]
PauliChainJoin[%]
δijδjk
δik
PauliChain[PauliEta[-I], PauliIndex[i0]] PIDelta[i0, i1] // FCI // PauliChainJoin
(η†)i1
PauliIndexDelta[PauliIndex[i2], PauliIndex[i3]] PauliIndexDelta[PauliIndex[i4], PauliIndex[i5]] PauliChain[PauliIndex[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]]
PauliChainJoin[%]
(ξ)i7(η†)i0δi2i3δi4i5(σa)i1i2(σb)i5i6(σ⋅p+m)i3i4
(ξ)i7(η†)i0(σa.(σ⋅p+m).σb)i1i6
PauliChainJoin[% PIDelta[i0, i1]]
(ξ)i7(η†.σa.(σ⋅p+m).σb)i6
PauliChainJoin[% PIDelta[i7, i6]]
η†.σa.(σ⋅p+m).σb.ξ