Chytov V. A dynamical symmetry breaking under the influence of an external gravitational and electromagnetic fields in the Numbu-Jona-Lasinio model and quadratic gravity

Object of investigation: a dynamical symmetry breaking in the Nambu-Jona-Lasinio model and quadratic gravity. Aim of investigation: to find the conditions of dynamical symmetry breaking in the twodimensional quadratic gravity with conformal gauge, to find the critical constant of interaction as a function of general covariant gauge parameters in four dimension space, to find the phase structure of the Nambu-Jona-Lasinio model with external grav-ity and electromagnetic fields. Methods of investigation: Schwinger-Dison equations, ladder approximation, effective potential of compound fields, nu-merical methods. Theoretical and practical results: the phase transition of the second order in 2-d conformal quadratic gravity is shown to take place, the dynamical mass is found as a function of the coupling constant as well as the critical constant; the critical coupling constant in 4-d gravity in covariant gauge don't depend on gauge parameters, the phase transition is the second order one; in the Nambu-Jona-Lasinio model the general expression for the effective potential of compound fermionic fields is obtained, the phase transitions in 3-, 4-, d- dimensional curved space with electromagnetic field are shown to take place, the phase structure is found. Fields of application: cosmology, black holes physics, astrophysics.