Confinement and dynamical chiral symmetry breaking in QED3.

We establish that QED3 can possess a critical number of flavors, Nfc, associated with dynamical chiral symmetry breaking if, and only if, the fermion wave function renormalization and photon vacuum polarization are homogeneous functions at infrared momenta when the fermion mass function vanishes. The Ward identity entails that the fermion-photon vertex possesses the same property and ensures a simple relationship between the homogeneity degrees of each of these functions. Simple models for the photon vacuum polarization and fermion-photon vertex are used to illustrate these observations. The existence and value of Nfc are contingent upon the precise form of the vertex but any discussion of gauge dependence is moot. We introduce an order parameter for confinement. Chiral symmetry restoration and deconfinement are coincident owing to an abrupt change in the analytic properties of the fermion propagator when a nonzero scalar self-energy becomes insupportable.