Dynamical Mass in Strongly Coupled QED

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 QED4, chiral symmetry is spontaneouly broken if α > αc(≃ π/3) in ladder approximation. The electron becomes massive, and is realized as Skyrmion in the low energy effective action. In QED3, electron gets dynmical mass in 1/N expansion if N < Nc(≃ 32/π2). With a Chern-Simons term, parity tends to break maximally in QED3. The quntum phase structure of QED3 with or without a Chern-Simons term is peculiar. Lecture given at 14th Symposium on Theoretical Physics, “Dynamical Symmetry Breaking and Effective Field Theory”, 21-27 July, 1995, Cheju, Korea E-mail address: [email protected]