Dynamical Symmetry Breaking in Four-Fermionic Models under the Influence of External Electromagnetic Field in Curved Spacetime

An investigation of the Nambu-Jona-Lasinio model with external constant electromagnetic and weak gravitational fields is carried out in three- and four-dimensional spacetimes. The effective potential of the composite bifermionic fields is calculated keeping terms linear in the curvature, while the electromagnetic field effect is treated exactly by means of the proper-time formalism. Numerical simulations of the dynamical symmetry breaking phenomenon accompanied by some phase transitions are presented.