Cadabra manual: Expand

expand_diracbar

Simplify the Dirac bar of a composite object.

Rewrite the Dirac conjugate of a product of spinors and gamma matrices as a product of Dirac and hermitean conjugates. This uses

$\begin{equation} \bar\psi = i \psi^\dagger\Gamma^0\,, \end{equation}$ together with

$\begin{equation} \Gamma_m^{\dagger} = \Gamma_0\Gamma_m\Gamma_0 \,. \end{equation}$ For example,

\bar{#}::DiracBar. \psi::Spinor(dimension=10). \Gamma{#}::GammaMatrix. ex:=\bar{\Gamma^{m n p} \psi};

$\displaystyle{}\bar{\Gamma^{m n p} \psi}$

expand_diracbar(_);

$\displaystyle{}\bar{\psi} \Gamma^{m n p}$