DiracIndexDelta
DiracIndexDelta[DiracIndex[i], DiracIndex[j]]
is the Kronecker-delta in the Dirac space with two explicit Dirac indices i
and j
.
See also
Overview, DiracChain, DCHN, DiracIndex, DIDelta, DiracChainJoin, DiracChainCombine, DiracChainExpand, DiracChainFactor.
Examples
DiracIndexDelta[DiracIndex[i], DiracIndex[j]]
δij
ex = DiracIndexDelta[DiracIndex[i], DiracIndex[j]]^2
δij2
4
DiracChainJoin[ex, TraceOfOne -> D]
D
ex = DiracIndexDelta[DiracIndex[i], DiracIndex[j]] DiracIndexDelta[DiracIndex[j], DiracIndex[k]]
δijδjk
δik
ex = DiracIndexDelta[DiracIndex[i2], DiracIndex[i3]] DiracIndexDelta[DiracIndex[i4], DiracIndex[i5]] DiracChain[DiracIndex[i7], Spinor[-Momentum[q], 0, 1]] DiracChain[Spinor[Momentum[p], m, 1], DiracIndex[i0]] DiracChain[DiracGamma[LorentzIndex[\[Mu]]], DiracIndex[i1], DiracIndex[i2]] DiracChain[DiracGamma[LorentzIndex[\[Nu]]], DiracIndex[i5], DiracIndex[i6]] DiracChain[m + DiracGamma[Momentum[p]], DiracIndex[i3], DiracIndex[i4]]
δi2i3δi4i5(γˉμ)i1i2(γˉν)i5i6(φ(−q))i7(γˉ⋅p+m)i3i4(φ(p,m))i0
(φ(−q))i7(φ(p,m))i0(γˉμ.(γˉ⋅p+m).γˉν)i1i6
DiracChainJoin[ex DIDelta[i0, i1]]
(φ(−q))i7(φ(p,m).γˉμ.(γˉ⋅p+m).γˉν)i6
DiracChainJoin[ex DIDelta[i7, i6]]
(φ(p,m))i0(γˉμ.(γˉ⋅p+m).γˉν.φ(−q))i1