We consider a superfield [itex]\Phi[/itex][itex]\left(x^{\mu}, \theta_{\alpha}\right)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

For a small variation [itex]\delta \Phi [/itex] = [itex] \bar{\epsilon} Q \Phi [/itex]

where the supercharge [itex]Q_{\alpha}[/itex] is given by:

[itex]Q_{\alpha}[/itex]=[itex]\frac{\partial}{\partial \bar{\theta}^{\alpha}}[/itex]-[itex]\left(\gamma^{\mu} \theta \right) _{\alpha} \partial _{\mu}[/itex]

They satisfy the algebra:

[itex]\left\{ Q_{\alpha}, Q_{\beta} \right\}[/itex] = -2[itex]\left( \gamma^{\mu} C \right)_{\alpha \beta} \partial_{\mu} [/itex]

where C is the charge coniugation matrix.

How can I demonstrate this? The exercise is to calculate explicitely the anticommutator.

Can you help me please?

Thank you very much!

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# Algebra of the generator of supersymmetry transformations?

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