On the triviality of textbook quantum electrodynamics

By adding a small, irrelevant four fermi interaction to the action of latti ce quantum electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. This allows an ab initio hig h precision, controlled study of the existence of "textbook" quantum electr odynamics with several species of fermions. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivi al. The logarithms of triviality, which modify mean field scaling laws, are pinpointed in several observables. The result supports Landau's contention that perturbative QED suffers from complete screening and would have a van ishing fine structure constant in the absence of a cutoff. (C) 2001 Publish ed by Elsevier Science B.V.