  We introduce a lattice model with local U(1) gauge symmetry which
incorporates explicit frustration in d >2. The form of the action is inspired
from the loop expansion of the fermionic determinant in standard lattice QED.
We study through numerical simulations the phase diagram of the model,
revealing the existence of a frustrated (antiferromagnetic) phase for d=3 and
d=4, once an appropriate order parameter is identified.
