DYNAMICAL SYMMETRY-BREAKING IN CURVED SPACETIME - 4-FERMION INTERACTIONS

This review deals with the theory of four-fermion interactions in curv ed spacetime. Starting with the D-dimensional Minkowski spacetime (2 l ess than or equal to D less than or equal to 4) the effective potentia l in the leading order of 1/N-expansion is calculated and the phase st ructure of the theory is investigated. Using the same technique the ef fective potential for composite operator <(psi)over bar psi> in four-f ermion models is calculated under the following circumstances: a) D-di mensional weakly curved spacetime (in linear curvature approximation), b) D-dimensional de Sitter and anti-de Sitter universe, c) D-dimensio nal Einstein universe. The phase structure of the theory is investigat ed analytically as well as numerically. Curvature induced phase transi tions are discussed where fermion masses are dynamically generated. As an extension of four-fermion models we consider the gauged Nambu-Jona -Lasinio (NJL) model, higher derivative NJL model and supersymmetric N JL model in weakly curved spacetime where the effective potential is a nalytically evaluated. The phase structure of the models is again anal yzed and the condition for the chiral symmetry breaking in the gauged NJL model is given in an analytical form. Finally the influence of two external effects (non-zero temperature and gravitational field, non-t rivial topology and gravitational field as well as magnetic and gravit ational field) to the phase structure of four-fermion models is analyz ed. The possibility of curvature and temperature-induced or curvature- and topology induced phase transitions is discussed. It is also argued that the chiral symmetry broken by a weak magnetic field may be resto red due to the presence of gravitational field. Some applications of f our-fermion models in quantum gravity are also briefly investigated.