Gauged Nambu–Jona-Lasinio studies of the triviality of quantum electrodynamics

By adding a small, irrelevant four-Fermi interaction to the action of noncompact lattice quantum electrodynamics (QED), the theory can be simulated with massless quarks in a vacuum free of lattice monopoles. Simulations directly in the chiral limit of massless quarks are done with high statistics on ${12}^4,$ ${16}^4,$ and ${20}^4$ lattices at a wide range of couplings with good control over finite size effects, systematic and statistical errors. The lattice theory possesses a second order chiral phase transition which we show is logarithmically trivial, with the same systematics as the Nambu–Jona-Lasinio model. The irrelevance of the four-Fermi coupling is established numerically. Our fits have excellent numerical confidence levels. The widths of the scaling windows are examined in both the coupling constant and bare fermion mass directions in parameter space. For a vanishing fermion mass we find a broad scaling window in coupling which is essential to the quality of our fits and conclusions. By adding a small bare fermion mass to the action we find that the width of the scaling window in the fermion mass direction is very narrow. Only when a subdominant scaling term is added to the leading term of the equation of state are adequate fits to the data possible. The failure of past studies of lattice QED to produce equation of state fits with adequate confidence levels to seriously address the question of triviality is explained. The vacuum state of the lattice model is probed for topological excitations, such as lattice monopoles and Dirac strings, and these objects are shown to be noncritical along the chiral transition line as long as the four-Fermi coupling is nonzero. Our results support Landau’s contention that perturbative QED suffers from complete screening and would have a vanishing fine structure constant in the absence of a cutoff.