Chiral symmetry breaking of strong coupling QED

The vacuum structure of strong coupling QED is investigated by means of the effective potential method. The introduction of the bilocal auxiliary fields enables us to path-integrate out the gauge and fermi fields and to obtain the effective action for the composite operators. The stationary equation for the potential is analyzed and the results are: (i) In the weak coupling phase, there exists only a trivial solution independent of gauge parameter. (ii) In the strong coupling phase, the nodeless chiral spontaneous breaking solution corresponds to the minimum vacuum energy in Landau gauge. It is stable under any fluctuations, with or without a small explicit breaking term. The scalar boson is a massive composite particle but the pseudoscalar boson is a massless Nambu-Goldstone particle. As the coupling constant tends to the critical coupling constant with a cutoff fixed, the mass of the scalar mode tends to zero; the 2nd order phase transition occurs. We also study the effect of explicit breaking. (author)