Dynamical mass generations and criticalvbehaviors in (2+1)-dimensional QED with the family of the four-fermion interaction

Abstract

We investigate the dynamical mass generation and critical behaviors in (2+1)-dimensional QED with the family of the four-fermion interaction. We construct the Dyson-Schwinger equation upto the order of 1/N and determine the fermion mass function ($\Sigma (p)$) and critical surface which separates the broken and unbroken phase, by solving the Dyson-Schwinger equation. We also consider the critical behaviors of the theory at finite temperature. The tadpole diagram which arises from the scalar-scalar type four-fermion interaction (($\bar{\psi}\pai)^2$) is the most dominant term in our Dyson-Schwinger equation, then we can see that the phase structures of the theory which contains the scalar-scalar type four-fermion interaction are mainly controled by the coupling of the scalar-scalar type four-fermion interaction. The vector-vector type four-fermion interaction (($\bar{\psi}\gamma_\mu\psi)^2$) improves the scale of the generated fermion mass and soften the dependence of the fermion flavor N in fermion mass function. In addition, we show that the ladder approximation can be adopted in the (2+1)-dimensional Dyson-Schwinger equation without infra-red divergence by introducing the Chern-Simons term. We also determine the critical temperature above which the broken U(1) $\otimes$ U(1) symmetry restores to U(2) symmetry by investigating the phase structures of the theory at finite temperature.