Wess Zumino model in two dimensions

alialice

1. The problem statement, all variables and given/known data

Hi!
I need some help to describe a Wess Zumino model in two dimensions:
spinors are real (because of the Majorana condition [itex]\theta=\theta^{\ast}[/itex]) and have two components;
the superfield is:
[itex] \phi \left( x,\theta\right)=A\left( x\right) + i\bar{\theta}\psi\left(x\right) +\frac{i}{2} \bar{\theta}\theta F\left(x\right)[/itex]
where:
A and F are scalars
ψ is a spinorial field.
The susy generator is:
[itex]Q_{\alpha}=\frac{\partial}{\partial \bar{\theta}^{\alpha}} -i \left(\gamma^{\mu} \right) _{\alpha} \partial_{\mu}[/itex]

1) What are the supersymmetry transformations of the fields?

2) Which is the invariant action of the model?

Thank you very much if you could give me some help!