We determine the critical fermion flavor for dynamical chiral symmetry breaking in three-dimensional quantum electrodynamics using nonlocal gauge (gauge parameter depends on the momentum or coordinate). The coupled Dyson–Schwinger equations of the fermion and gauge boson propagators are considered in the vicinity of the critical point. Illustrated by using the transverse vertex proposed by Bashir et al., we show that: for a variety of the transverse vertex, the critical flavor is still 128/3π2, the same as using the bare vertex.
We study the chiral symmetry-breaking (2 + 1)-dimensional quantum electrodynamics with four-fermion interactions. Solving the Dyson–Schwinger equation with a boundary condition identical to an equation of state, we determine the phase diagram of this model and obtain a large anomalous dimension of the operator [Formula: see text]. By substituting a. symmetry-breaking solution in the equation of state, we find the critical exponents and show that they satisfy the hyperscaling laws. Some comments are given on the equation of hierarchy between the chiral symmetry-breaking scale and the fundamental scale in our model.
On the basis of Bethe-Salpeter equations for electron-positron bound states in strong-coupling quantum electrodynamics with additional four-fermion interactions, the formula for the critical line dividing the chiral-symmetry-breaking phase from the symmetric phase is derived. The beta functions near the critical line are calculated explicitly and the phase structure is discussed based on these beta functions.
Chiral symmetry breaking in three-dimensional quantum electrodynamics in the presence of irrelevant interactions: A renormalization group study