Wess Zumino model in two dimentions

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Hi!
I need some help to describe a Wess Zumino model in two dimensions: spinors are real (because of the Majorana condition) and the superfield is:
\phi\left(x,\theta \right)= A(x) + i \bar{\theta} \psi(x) + \frac{1}{2} i \bar{\theta} θ F(x)
where:
A and F are scalar
ψ is a spinorial field
1) What are the supersymmetry transformations of the fields?
The susy generator is:
Q_{\alpha} = \frac{\partial}{\partial \bar{\theta^{\alpha}}} - i (\gamma_{\mu} \theta )_{\alpha} \partial_{\mu}
2) Which is the invariant action of the model?
Thank you very much if you could give me some help! :smile:
 
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