Welcome to Cadabra Q&A, where you can ask questions and receive answers from other members of the community.
0 votes

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)$.

asked in Feature requests by (240 points)
edited by

Do you mean that the two other spinor indices are 'free', not implicitly contracted with spinor objects?

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)$.

Please log in or register to answer this question.

...