FeynCalc manual (development version)

DiracSigmaExpand

DiracSigmaExpand[exp] applies linearity to the arguments of DiracSigma.

See also

Overview, DiracGamma, DiracSigma.

Examples

DiracSigma[GSD[p] + GSD[q], GSD[r]] 
 
ex = % // DiracSigmaExpand

DiracSigma(γp+γq,γr)\text{DiracSigma}(\gamma \cdot p+\gamma \cdot q,\gamma \cdot r)

σpr+σqr\sigma ^{pr}+\sigma ^{qr}

ex // FCE // StandardForm

(*DiracSigma[GSD[p], GSD[r]] + DiracSigma[GSD[q], GSD[r]]*)

Notice that DiracSigmaExpand does not expand Dirac matrices contracted to linear combinations of 44-vectors by default.

DiracSigma[GSD[p + q], GSD[r]] 
 
DiracSigmaExpand[%]

σp+qr\sigma ^{p+qr}

σp+qr\sigma ^{p+qr}

If such expansions are required, use the option DiracGammaExpand.

DiracSigmaExpand[DiracSigma[GSD[p + q], GSD[r]], DiracGammaExpand -> True]

σpr+σqr\sigma ^{pr}+\sigma ^{qr}

The option Momentum allows us to perform more fine-grained expansions of DiracSigma.

DiracSigma[GSD[p], GSD[r] + GSD[t]] + DiracSigma[GSD[l] + GSD[n], GSD[p]] 
 
DiracSigmaExpand[%, Momentum -> {r}]

DiracSigma(γl+γn,γp)+DiracSigma(γp,γr+γt)\text{DiracSigma}(\gamma \cdot l+\gamma \cdot n,\gamma \cdot p)+\text{DiracSigma}(\gamma \cdot p,\gamma \cdot r+\gamma \cdot t)

DiracSigma(γl+γn,γp)+σpr+σpt\text{DiracSigma}(\gamma \cdot l+\gamma \cdot n,\gamma \cdot p)+\sigma ^{pr}+\sigma ^{pt}