The Schwinger function in the Nambu-Jona-Lasinio model

Tag der Einreichung: According to arguments made by Gribov, if the backreaction of pions, the Goldstone bosons of chiral symmetry breaking, is taken into account, the analytic properties of the quark propagator change in a way that positivity of the Schwinger function might be violated. If this is the case, this violation can be interpreted as an explanation of confinement in QCD then. For QCD this has been investigated in [1] but the positivity violation due to pion loops did not occur. Although the NJL-model is has no confinement in Hartree approximation, it might be interesting to investigate if positivity is violated in this model if a pion loop is taken into account. This investigation is done here. We will see at the end of this work that Gribov’s confinement scenario is not realized in the NJL model, which agrees with the fact that the NJL model is expected to have no confinement mechanism. 2 Content