sort_spinors
Sort Majorana spinor bilinears
Sorts Majorana spinor bilinears using the Majorana flip property,
which for anti-commuting spinors takes the form
\begin{equation}
\bar\psi_1 \Gamma_{r_1\cdots r_n}\psi_2 =
\alpha \beta^n (-)^{\frac{1}{2}n(n-1)}\, \bar\psi_1
\Gamma_{r_1\cdots r_n}\psi_2\, .
\end{equation}
Here $\alpha$ and $\beta$ determine the properties of the charge
conjugation matrix,
\begin{equation}
{\cal C}^T = \alpha {\cal C}\,,\quad
{\cal C}\Gamma_r {\cal C}^{-1} = \beta \Gamma_r^T\, .
\end{equation}
Here is an example.{\chi, \psi, \psi_{m}}::Spinor(dimension=10, type=MajoranaWeyl).
{\chi, \psi, \psi_{m}}::AntiCommuting.
\bar{#}::DiracBar.
\Gamma{#}::GammaMatrix.
{\psi_{m}, \psi, \chi}::SortOrder.
ex:=\bar{\chi} \Gamma_{m n} \psi;
\(\displaystyle{}\bar{\chi} \Gamma_{m n} \psi\)
sort_spinors(_);
\(\displaystyle{}-\bar{\psi} \Gamma_{m n} \chi\)