FeynCalc manual (development version)

DiracSubstitute5

DiracSubstitute5[exp] rewrites γ5\gamma^5 in terms of the chirality projectors γ6\gamma^6 and γ7\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[%]

γˉ5\bar{\gamma }^5

γˉ6γˉ7\bar{\gamma }^6-\bar{\gamma }^7

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

uˉ(p1).γˉμ.γˉ5.γˉν.u(p2)\bar{u}\left(p_1\right).\bar{\gamma }^{\mu }.\bar{\gamma }^5.\bar{\gamma }^{\nu }.u\left(p_2\right)

(φ(p1)).γˉμ.(γˉ6γˉ7).γˉν.(φ(p2))\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)