\cdbproperty{AntiCommuting}{}

Makes components anti-commuting. Example:
\begin{screen}{1,2}
{A,B}::AntiCommuting.
B A;
@prodsort!(%);
(-1) A B;
\end{screen}
It also works for objects with indices:
\begin{screen}{1,2}
{\psi_{m}, \chi}::AntiCommuting.
\psi_{m} \chi \psi_{n};
@prodsort!(%);
(-1) \chi \psi_{m} \psi_{n};
\end{screen}
If you want a pattern like \verb|\psi_{m}| to anti-commute with
itself, you should use the \subsprop{SelfAntiCommuting} property instead.

You can think about the difference
between \subsprop{SelfAntiCommuting} and \subsprop{AntiCommuting} in
the following way. If \verb|A_{m n}| is \verb|SelfAntiCommuting|, it
means that for each value of the indices the expression \verb|A_{m n}|
is an operator which anti-commutes with the operator for any other
value of the indices. The matrix~$A$ is thus a matrix of
operator-valued components which mutually anti-commute. On the other
hand, if \verb|A| and \verb|B| are declared to
be \verb|AntiCommuting|, then these can be viewed as two matrices of
commuting components, whose matrix product satisfies~$A B = - B A$.

If you attach the \verb|AntiCommuting| property to an object
with an \subsprop{ImplicitIndex} property, the commutation property does
not refer to the object as a whole, but rather to its components. The
logic behind that becomes clear when considering e.g.~spinor bilinears
\begin{screen}{1,2,3,4,5,6,7,9}
{\chi, \psi}::Spinor(dimension=10, type=MajoranaWeyl).
{\chi, \psi}::AntiCommuting.
\bar{#}::DiracBar.
\Gamma{#}::GammaMatrix.
{\chi, \psi}::SortOrder.
\bar{\psi} \Gamma_{m n p} \chi;
@prodsort!(%);
@prodsort: not applicable.
@spinorsort!(%);
\bar{\chi} \Gamma_{m n p} \psi;
\end{screen}
Here \subscommand{prodsort} did not act because both the spinors and
the gamma matrices have the \subsprop{ImplicitIndex} property and
there are thus no simple rules for their re-ordering. However,
the \subscommand{spinorsort} algorithm did act, and took into account
the fact that the components of the spinors are anti-commuting.

\cdbseealgo{prodsort}
\cdbseealgo{spinorsort}
\cdbseeprop{SelfAntiCommuting}
\cdbseeprop{Commuting}
\cdbseeprop{ImplicitIndex}
