FeynCalc manual (development version)

Anti5

Anti5[exp] anticommutes all γ5\gamma^5 in exp to the right. Anti5[exp, n] anticommutes all γ5\gamma^5 nn-times to the right. Anti5[exp, -n] anticommutes all γ5\gamma^5 nn-times to the left.

See also

Overview, DiracOrder, DiracSimplify, DiracTrick.

Examples

GA[5, \[Mu]] 
 
Anti5[%] 
 
Anti5[%, -1]

γˉ5.γˉμ\bar{\gamma }^5.\bar{\gamma }^{\mu }

γˉμ.γˉ5-\bar{\gamma }^{\mu }.\bar{\gamma }^5

γˉ5.γˉμ\bar{\gamma }^5.\bar{\gamma }^{\mu }

GA[5, \[Alpha], \[Beta], \[Gamma], \[Delta]] 
 
Anti5[%, 2] 
 
Anti5[%%, Infinity] 
 
Anti5[%, -Infinity]

γˉ5.γˉα.γˉβ.γˉγ.γˉδ\bar{\gamma }^5.\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }.\bar{\gamma }^{\gamma }.\bar{\gamma }^{\delta }

γˉα.γˉβ.γˉ5.γˉγ.γˉδ\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }.\bar{\gamma }^5.\bar{\gamma }^{\gamma }.\bar{\gamma }^{\delta }

γˉα.γˉβ.γˉγ.γˉδ.γˉ5\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }.\bar{\gamma }^{\gamma }.\bar{\gamma }^{\delta }.\bar{\gamma }^5

γˉ5.γˉα.γˉβ.γˉγ.γˉδ\bar{\gamma }^5.\bar{\gamma }^{\alpha }.\bar{\gamma }^{\beta }.\bar{\gamma }^{\gamma }.\bar{\gamma }^{\delta }

In the naive γ5\gamma^5-scheme DD-dimensional γ\gamma-matrices anticommute with γ5\gamma^5.

GA5 . GAD[\[Mu]] 
 
Anti5[%]

γˉ5.γμ\bar{\gamma }^5.\gamma ^{\mu }

γμ.γˉ5-\gamma ^{\mu }.\bar{\gamma }^5

Anti5 also works in the t’Hooft-Veltman-Breitenlohner-Maison scheme

FCSetDiracGammaScheme["BMHV"]; 
 
Anti5[GA5 . GAD[\[Mu]]]

2γ^μ.γˉ5γμ.γˉ52 \hat{\gamma }^{\mu }.\bar{\gamma }^5-\gamma ^{\mu }.\bar{\gamma }^5

FCSetDiracGammaScheme["NDR"];