Dynamical Mass in Strongly Coupled QED

Abstract

We review dynamical mass generation in three and four dimensional Ableian gauge theories. The basic approach analyzed here is to solve Schwinger-Dyson equations in some approximations. In both cases, the coupling has to be larger than a critical value to have dynamical symmetry breaking. In $QE{D}_4$, chiral symmetry is spontaneouly broken if $\alpha >{\alpha }_c(\simeq \pi /3)$ in ladder approximation. The electron becomes massive, and is realized as Skyrmion in the low energy effective action. In $QE{D}_3$, electron gets dynmical mass in $1/N$ expansion if $N<N_c(\simeq 32/{\pi }^2)$. With a Chern-Simons term, parity tends to break maximally in $QE{D}_3$. The quntum phase structure of $QE{D}_3$ with or without a Chern-Simons term is peculiar.

29 pages, LaTeX 2e, To appear in Proc. 14th Symposium on Theoretical Physics ``Dynamical Symmetry Breaking and Effective Field Theory'', Cheju, Korea, July 21-26, 1995