  Using the example of compact U(1) lattice gauge theory we argue that quantum
link models can be used to reproduce the physics of conventional Hamiltonian
lattice gauge theories. In addition to the usual gauge coupling $g$, these
models have a new parameter $j$ which naturally cuts-off large electric flux
quanta on each link while preserving exact U(1) gauge invariance. The
$j\to\infty$ limit recovers the conventional Hamiltonian. At strong couplings,
the theory shows confinement and chiral symmetry breaking for all non-trivial
values of $j$. The phase diagram of the 3+1 dimensional theory suggests that a
coulomb phase is present at large but finite $j$. Setting $g=0$, a new approach
to the physics of compact U(1) gauge theory on the lattice emerges. In this
case the parameter $j$ takes over the role of the gauge coupling, and $j\to
\infty$ describes free photons.
