We consider a theory described by the Lagrangian,

$$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$

The corresponding field equations are,
$$(i\gamma^\mu\partial_\mu-m+g\bar{\Psi}\Psi)\Psi=0$$

Could this model have soliton solutions? Without the last term, it is just a Dirac field (if $g=0$), but it has to be included. This is similar to the Thirring model. I was looking for this field in books and papers but I haven't found it. If you know about it could you give me any reference?

This post imported from StackExchange Physics at 2014-06-25 21:06 (UCT), posted by SE-user Anthonny