A nonlocal, covariant generalisation of the NJL model

We solve a nonlocal generalisation of the NJL model in the Hartree approximation. This model has a separable interaction, as suggested by instanton models of the QCD vacuum. The choice of form factor in this interaction is motivated by the confining nature of the vacuum. A conserved axial current is constructed in the chiral limit of the model and the pion properties are shown to satisfy the Gell-Mann–Oakes–Renner relation. For reasonable values of the parameters the model exhibits quark confinement.