Is Thirring model a particular case of Gross model?

Look at this: http://en.wikipedia.org/wiki/Gross-Neveu_model

Wikipedia sais "When N=1 it reduces to the integrable Thirring model". but the aditional term in thirring model is $\frac{g}{2}\left(\overline{\psi}\gamma^\mu\psi\right) \left(\overline{\psi}\gamma_\mu \psi\right)$ I think this is different from $\frac{1}{2}g \left(\overline{\psi} \psi\right)^2$ the aditional term of Gross.Neveu model. So I think wikipedia is wrong. Am I right?

if you do not mind I would like that you respond to this question also Could this model have soliton solutions?

Thanks in advance.

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1 Answer

Yes, because the grassman expansion of a quartic fermi interaction can only be $\psi_1\psi_2\bar{\psi}_1\bar{\psi}_2$ in 2d, because there are only four grassman fields, so all other quartics are zero.

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@James: Thanks, I should have fixed it--- it was a phone answer (no dollar signs available). –  Ron Maimon Jan 25 '12 at 5:38