  In a previous paper we have shown how the Wilsonian renormalization group
naturally leads to the equivalence of the standard QED with a matter-only
theory. In this paper we give an improved explanation of the equivalence and
discuss, as an example, the equivalence of a chiral QED in the Higgs phase with
a matter-only theory. Ignoring the contributions suppressed by the negative
powers of a UV cutoff, the matter-only theory is equivalent to the
perturbatively renormalizable chiral QED with two complex Higgs fields. In the
matter-only theory chiral anomaly arises without elementary gauge fields.
