DIDelta
DIDelta[i, j]
is the Kronecker-delta in the Dirac space.
DIDelta[i,j]
is transformed into DiracDelta[DiracIndex[i],DiracIndex[j]]
by FeynCalcInternal
.
See also
Overview, DiracChain, DCHN, DiracIndex, DiracIndexDelta, DiracChainJoin, DiracChainExpand, DiracChainFactor.
Examples
δij
DIDelta[i, i]
DiracChainJoin[%]
δii
4
DIDelta[i, j]^2
DiracChainJoin[%]
δij2
4
DIDelta[i, j] DIDelta[j, k]
DiracChainJoin[%]
δijδjk
δik
ex = DCHN[SpinorUBar[p, m], i0] DCHN[GA[\[Mu]], i1, i2] DCHN[GS[p] + m, i3, i4] DCHN[GA[\[Nu]], i5, i6] DIDelta[i2, i3] DIDelta[i4, i5] DCHN[i7, SpinorV[q]]
δi2i3δi4i5(v(q))i7(γˉμ)i1i2(γˉν)i5i6(uˉ(p,m))i0(γˉ⋅p+m)i3i4
ex // FCI // StandardForm
(*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]] DiracIndexDelta[DiracIndex[i2], DiracIndex[i3]] DiracIndexDelta[DiracIndex[i4], DiracIndex[i5]]*)
(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