On mirror symmetry in three dimensional abelian gauge theories

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