Cadabra
a field theory motivated approach to computer algebra

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(_);
\(\displaystyle{}\bar{\psi} \Gamma^{m n p}\)
Copyright © 2001-2017 Kasper Peeters
Questions? info@cadabra.science