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The real-time formalism at finite temperature and chemical potential for thenonlocal Nambu--Jona-Lasinio model is developed in the presence of a Gaussiancovariant regulator. We construct the most general thermal propagator, by meansof the spectral function. As a result, the model involves the propagation ofmassive quasiparticles. The appearance of complex poles is interpreted as aconfinement signal, and in this case we have unstable quasiparticles with afinite decay width. An expression for the propagator along the critical line,where complex poles start to appear, is also obtained. A generalization toother covariant regulators is proposed.

Thermal nonlocal Nambu--Jona-Lasinio model in the real time formalism