We explore the compact U(1) lattice gauge theory with staggered fermio
ns and gauge field action - Sigma(p)[beta cos(Theta p) + gamma cos(2 T
heta p)], both for dynamical fermions and in the quenched approximatio
n. (Theta p denotes the plaquette angle.) In simulations with dynamica
l fermions at various gamma less than or equal to -0.2 on 6(4) lattice
s we find the energy gap at the phase transition of a size comparable
to the pure gauge theory for gamma less than or equal to 0 on the same
lattice, diminishing with decreasing gamma. This suggests a second-or
der transition in the thermodynamic limit of the theory with fermions
for gamma below some finite negative value. Studying the theory on lar
ge lattices at gamma = -0.2 in the quenched approximation by means of
the equation of state we find non-Gaussian values of the critical expo
nents associated with the chiral condensate, beta(chi) similar or equa
l to 0.32 and delta similar or equal to 1.8, and determine the scaling
function. Furthermore, we evaluate the meson spectrum and study the P
CAC relation. (C) 1998 Elsevier Science B.V.