We review our analysis of the strong coupling of compact QED on a lattice
with staggered Fermions. We show that, for infinite coupling, compact QED is
exactly mapped in a quantum antiferromagnet. We discuss some aspects of this
correspondence relevant for effective field theories of Josephson junctions
arrays.Comment: 33 pages,latex,Proceedings of "Common Trends in Condensed Matter and
High Energy Physics",DFUPG 1/9