Schwinger-Dyson Equations in 2D Induced Gravity in Covariant Gauges

We formulate the Schwinger-Dyson equations in the ladder approximation for 2D induced quantum gravity with fermions using covariant gauges of harmonic type. It is shown that these equations can be formulated consistently in a gauge of Landau type (for negative cosmological constant). A numerical analysis of the equations hints towards the possibility of chiral symmetry breaking, depending on the value of the coupling constant.Comment: 11 pages, LaTeX file, 2 figures (available upon request), 94/7/2

Chiral Symmetry Breaking in the d=3d=3 Nambu-Jona-Lasinio Model in Curved Spacetime

The phase structure of the $d=3$ Nambu-Jona-Lasinio model in curved spacetime is considered to leading order in the $1/N$--expansion and in the linear curvature approximation. The possibility of a curvature-induced first-order phase transition is investigated numerically. The dynamically generated fermionic mass is calculated for some values of the curvature.Comment: 7 pages, LaTeX file, 4 figures (appended as compressed postscript file), Jan. 199

Dynamical symmetry restoration for a higher-derivative four-fermion model in an external electromagnetic field

A four-fermion model with additional higher-derivative terms is investigated in an external electromagnetic field. The effective potential in the leading order of large-N expansion is calculated in external constant magnetic and electric fields. It is shown that, in contrast to the former results concerning the universal character of "magnetic catalysis" in dynamical symmetry breaking, in the present higher-derivative model the magnetic field restores chiral symmetry broken initially on the tree level. Numerical results describing a second-order phase transition that accompanies the symmetry restoration at the quantum level are presented.Comment: LaTeX, 14 pages, 4 ps-figure

Dynamical symmetry breaking in the external gravitational and constant magnetic fields

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetrybreaking. As simple models of the dynamical symmetry breaking we consider the Nambu-Jona-Lasinio (NJL) model and the supersymmetric Nambu-Jona-Lasinio (SUSY NJL) model non-minimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found up to the linear terms on the spacetime curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved spacetime. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken chiral symmetry phase due to the fixed magnetic field makes this phase to be less broken. On the same time strong magnetic field quickly induces chiral symmetry breaking even at the presence of fixed gravitational field within nonbroken phase.Comment: 23 pages, Latex, epic.sty and eepic.sty are use

Chiral symmetry breaking in d=3 NJL model in external gravitational and magnetic fields

The phase structure of $d=3$ Nambu-Jona-Lasinio model in curved spacetime with magnetic field is investigated in the leading order of the $1/N$-expansion and in linear curvature approximation (an external magnetic field is treated exactly). The possibility of the chiral symmetry breaking under the combined action of the external gravitational and magnetic fields is shown explicitly. At some circumstances the chiral symmetry may be restored due to the compensation of the magnetic field by the gravitational field.Comment: 7 pages, LaTe

Dynamical symmetry breaking in the Nambu-Jona-Lasino model with external gravitational and constant electric fields

An investigation of the Nambu-Jona-Lasino model with external constant electric 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 exactly 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.Comment: 20 pages, LaTeX, 6 .ps-figures, Final version published in "Classical and Quantum Gravity