Cadabra manual: SelfAntiCommuting

SelfAntiCommuting

Make components of tensors anti-commute.

Used to make objects with indices anti-commuting when their index values are different. Example:

\psi^{\mu}::SelfAntiCommuting. ex:= \psi^{\nu} \psi^{\mu};

\(\displaystyle{}\psi^{\nu} \psi^{\mu}\)

canonicalise(_);

\(\displaystyle{}-\psi^{\mu} \psi^{\nu}\)

ex:= \psi^{\mu} \psi^{\mu};

\(\displaystyle{}\psi^{\mu} \psi^{\mu}\)

canonicalise(_);

\(\displaystyle{}0\)

This could not be handled with AntiCommuting because that property handles the behaviour of different expression patterns.