Thermo-magnetic nonlocal NJL model in the real and imaginary time formalisms

Abstract

In this paper, we study a nonlocal Nambu–Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. By working in the real time formalism and computing the spectral density function, we find that the effect of the magnetic field on the poles of the propagator can be entirely absorbed within the mean field value of the scalar field. The analytic structure of our propagator is then preserved in the weak magnetic field limit. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It is also found that the magnetic field enhances the thermodynamical instability of the system. We work in the weak field limit, i.e. [Formula: see text]. At this level there is no splitting of the critical temperatures for chiral and deconfinement phase transitions.