FeynCalc manual (development version)

DiracMatrix

DiracMatrix[mu] denotes a Dirac gamma matrix with Lorentz index μ\mu.

DiracMatrix[mu , nu , ...] is a product of γ\gamma matrices with Lorentz indices mu , nu , ...

DiracMatrix[5] is γ5\gamma ^5.

DiracMatrix[6] is (1+γ5)/2(1 + \gamma^5)/2.

DiracMatrix[7] is (1γ5)/2(1 - \gamma^5)/2.

The shortcut DiracMatrix is deprecated, please use GA instead!

See also

Overview, GA, FCI.

Examples

DiracMatrix[\[Mu]]

γˉμ\bar{\gamma }^{\mu }

This is how to enter the non-commutative product of two. The Mathematica Dot “.” is used as non-commutative multiplication operator.

DiracMatrix[\[Mu]] . DiracMatrix[\[Nu]]

γˉμ.γˉν\bar{\gamma }^{\mu }.\bar{\gamma }^{\nu }

DiracMatrix[\[Alpha]] // StandardForm

(*DiracGamma[LorentzIndex[\[Alpha]]]*)

DiracMatrix is scheduled for removal in the future versions of FeynCalc. The safe alternative is to use GA.

GA[\[Mu]]

γˉμ\bar{\gamma }^{\mu }

GAD[\[Mu]]

γμ\gamma ^{\mu }

FCI[GA[\[Mu]]] === DiracMatrix[\[Mu]]

True\text{True}

FCI[GAD[\[Mu]]] === DiracMatrix[\[Mu], Dimension -> D]

True\text{True}