Monday, June 23, 2014

quantum field theory - Could this model have soliton solutions?



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?




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