FeynCalc manual (development version)

DiracSubstitute5

DiracSubstitute5[exp] rewrites $\gamma^5$ in terms of the chirality projectors $\gamma^6$ and $\gamma^7$. DiracSubstitute5 is also an option of various FeynCalc functions that handle Dirac algebra.

See also

Overview, DiracSubstitute67, DiracGamma, ToDiracGamma67.

Examples

GA[5] 
 
DiracSubstitute5[%]

$$\bar{\gamma }^5$$

$$\bar{\gamma }^6-\bar{\gamma }^7$$

SpinorUBar[Subscript[p, 1]] . GA[\[Mu]] . GA[5] . GA[\[Nu]] . SpinorU[Subscript[p, 2]] 
 
DiracSubstitute5[%]

$$\bar{u}\left(p_1\right).\bar{\gamma }^{\mu }.\bar{\gamma }^5.\bar{\gamma }^{\nu }.u\left(p_2\right)$$

$$\left(\varphi (\overline{p}_1)\right).\bar{\gamma }^{\mu }.\left(\bar{\gamma }^6-\bar{\gamma }^7\right).\bar{\gamma }^{\nu }.\left(\varphi (\overline{p}_2)\right)$$