FeynCalc manual (development version)

DiracSubstitute67

DiracSubstitute67[exp] inserts the explicit definitions of the chirality projectors $\gamma^6$ and $\gamma^7$. DiracSubstitute67 is also an option of various FeynCalc functions that handle Dirac algebra.

See also

Overview, DiracSubstitute5, DiracGamma, ToDiracGamma67.

Examples

DiracGamma[6] 
 
DiracSubstitute67[%]

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

$$\frac{\bar{\gamma }^5}{2}+\frac{1}{2}$$

DiracGamma[7] 
 
DiracSubstitute67[%]

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

$$\frac{1}{2}-\frac{\bar{\gamma }^5}{2}$$

SpinorUBar[Subscript[p, 1]] . GA[6] . SpinorU[Subscript[p, 2]] 
 
DiracSubstitute67[%]

$$\bar{u}\left(p_1\right).\bar{\gamma }^6.u\left(p_2\right)$$

$$\left(\varphi (\overline{p}_1)\right).\left(\frac{\bar{\gamma }^5}{2}+\frac{1}{2}\right).\left(\varphi (\overline{p}_2)\right)$$

SpinorUBar[Subscript[p, 1]] . GA[7] . SpinorU[Subscript[p, 2]] 
 
DiracSubstitute67[%]

$$\bar{u}\left(p_1\right).\bar{\gamma }^7.u\left(p_2\right)$$

$$\left(\varphi (\overline{p}_1)\right).\left(\frac{1}{2}-\frac{\bar{\gamma }^5}{2}\right).\left(\varphi (\overline{p}_2)\right)$$