Abstract
We present an identity relating the partition function of
= 4 supersymmetric QED to that of its dual under mirror symmetry.
The identity is a generalized Fourier transform. Many known
properties of abelian theories can be derived from this formula,
including the mirror transforms for more general gauge and matter
content. We show that = 3 Chern-Simons QED and = 4 QED with
BF-type couplings are conformal field theories with exactly marginal
couplings. Mirror symmetry acts on these theories as strong-weak
coupling duality. After identifying the mirror of the gauge coupling
(sometimes called the ``magnetic coupling'') we construct a theory
which is exactly mirror - at all scales - to = 4 SQED.
We also study vortex-creation operators in the large Nf limit.