Hi everyone,

Is there a way to perform a Fierz transformation on a product of **two** spinors?

Thanks.

Edit:

For example, if we have the majonara spinors $\chi^{\sigma} = \bar{\chi} = \bar{\lambda} P_{L}$ and $\varphi_{\alpha} = \varphi = P_{L} \chi$, where $P_{L} = \frac{1}{2} (1 + \gamma_{*}) $, the fierz identity for $\varphi \bar{\chi}$ is $ \varphi \bar{\chi} = -\frac{1}{2} P_{L} (\bar{\lambda} P_{L} \chi) + \frac{1}{8} P_{L} (\gamma_{\mu \nu} \bar{\lambda} \gamma^{\mu \nu} P_{L} \chi)$.