FeynCalc manual (development version)

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]]

\delta _{ij}

ex = DiracIndexDelta[DiracIndex[i], DiracIndex[j]]^2

\delta _{ij}^2

DiracChainJoin[ex]

4

DiracChainJoin[ex, TraceOfOne -> D]

D

ex = DiracIndexDelta[DiracIndex[i], DiracIndex[j]] DiracIndexDelta[DiracIndex[j], DiracIndex[k]]

\delta _{ij} \delta _{jk}

DiracChainJoin[ex]

\delta _{ik}

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]]

\delta _{\text{i2}\;\text{i3}} \delta _{\text{i4}\;\text{i5}} \left(\bar{\gamma }^{\mu }\right){}_{\text{i1}\;\text{i2}} \left(\bar{\gamma }^{\nu }\right){}_{\text{i5}\;\text{i6}} \left(\varphi (-\overline{q})\right)_{\text{i7}} \left(\bar{\gamma }\cdot \overline{p}+m\right)_{\text{i3}\;\text{i4}} \left(\varphi (\overline{p},m)\right)_{\text{i0}}

DiracChainJoin[ex]

\left(\varphi (-\overline{q})\right)_{\text{i7}} \left(\varphi (\overline{p},m)\right)_{\text{i0}} \left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }\right){}_{\text{i1}\;\text{i6}}

DiracChainJoin[ex DIDelta[i0, i1]]

\left(\varphi (-\overline{q})\right)_{\text{i7}} \left(\varphi (\overline{p},m).\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }\right){}_{\text{i6}}

DiracChainJoin[ex DIDelta[i7, i6]]

\left(\varphi (\overline{p},m)\right)_{\text{i0}} \left(\bar{\gamma }^{\mu }.\left(\bar{\gamma }\cdot \overline{p}+m\right).\bar{\gamma }^{\nu }.\varphi (-\overline{q})\right){}_{\text{i1}}