arXiv:hep-th/9710203v3 13 May 1998 Dynamical symmetry breaking in the Nambu-Jona-Lasinio model with external gravitational and constant electric fields E. Elizalde 1,2,∗ , Yu. I. Shil’nov 1,3,† and V. V. Chitov 3,‡ 1 Consejo Superior de Investigaciones Cient´ ıficas, IEEC, Edifici Nexus-204, Gran Capit` a 2-4, 08034, Barcelona, Spain 2 Department ECM, Faculty of Physics, University of Barcelona, Diagonal 647, 08028, Barcelona, Spain 3 Department of Theoretical Physics, Faculty of Physics, Kharkov State University, Svobody Sq. 4, 310077, Kharkov, Ukraine Abstract An investigation of the Nambu-Jona-Lasino model with external constant elec- tric 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 electric field effect is treated ex- actly by means of the proper-time formalism. A rich dynamical symmetry breaking pattern, accompanied by phase transitions which are ruled, independently, by both the curvature and the electric field strength is found. Numerical simulations of the transitions are presented. PACS numbers: 1115E, 0462, 1125, 1130R, 1210. * E-mail: eli@zeta.ecm.ub.es, elizalde@io.ieec.fcr.es † Present e-mail: visit2@ieec.fcr.es ‡ E-mail: chitov@io.itl.net.ua 1