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According to Ryder Quantum Field Theory page 440 the "simplified Wess-Zumino model" has the lagrangian $$ \mathscr{L} = \frac{1}{2}(\partial_\mu A)^2 + \frac{1}{2}(\partial_\mu B)^2 + \frac{1}{4} \bar{\Psi} i \gamma^\mu \overleftrightarrow{\partial}_\mu \Psi .\tag{11.92}$$ After some calculations Ryder has the necessity to introduce two other auxiliary fields $F$ and $G$ (page 448) so that the "final lagrangian" is $$ \mathscr{L} = \frac{1}{2}(\partial_\mu A)^2 + \frac{1}{2}(\partial_\mu B)^2 + \frac{1}{4} \bar{\Psi} i \gamma^\mu \overleftrightarrow{\partial}_\mu \Psi + \frac{1}{2}F^2 + \frac{1}{2} G^2 .\tag{11.144}$$ My question is: is this lagrangian with the four scalar fields the Wess-Zumino model? Or it is still the "simplified one"?

I could not find in Google the "simplified model" and the "posta model" (the term "posta" means the real one, it is a word we use very often in my country).

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The models (11.144) & (11.92) are called the free massless Wess-Zumino model with or without auxiliary fields, respectively. The point being that the SUSY algebra is realized off-shell and only on-shell, respectively. The word simplified seems to be non-standard terminology by Ryder.

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  • $\begingroup$ Thanks! So I think that the "non-simplified model" is the one with mass and/or interactions. $\endgroup$ – user171780 Sep 3 '18 at 12:05

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