Chiral symmetry breaking and restoration at finite temperature in quantum electrodynamics with a four-fermion interaction

Abstract

Using the ladder approximation, we discuss chiral symmetry breaking in four-dimensional QED with a chirally invariant four-fermion interaction. From the analyses of the Schwinger-Dyson equation for the fermion mass function, we show that the fermion mass can be dynamically generated and obtain the critical line which separates the broken phase from the symmetric one in the framework of the gauge and four-fermion couplings. We also consider the theory at finite temperature. In a constant (momentum independent) mass limit, the critical temperature for the restoration of chiral symmetry is derived. In a 1/N expansion, we study chiral symmetry breaking in three-dimensional QED with a chirally invariant four-fermion interaction. Similar to four-dimensional theory, there exist the critical exponents which quantify the critical behavior of different physical quantities. We also discuss the basic behavior of the dynamical mass scale $Sigma$(0) near the critical line in the theory. Various expressions for the dynamical mass scale were obtained on diferent approaches to the critical line. Using the 1/N expansion, we derive the temperature dependent Schwinger-Dyson equation for the dynamically generated fermion mass of three-dimensional QED with the chirally invariant four-fermion interaction. We firstly anlayze it in the constant mass limit and then generalize it to the case of the momentum dependent fermion mass function. Solving the equations numerically, we obtain the critical temperature above which chiral symmetry is restored and the dynamical fermion mass that depends on temperature.