What is the most general Abelian gauge theory in two spatial dimensions?

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Abstract
On the basis of a few assumptions as to the desired ingredients of a gauge theory in 2+1 space, the most general Abelian gauge theory is derived. It is seen to include in special limits (a) electrodynamics (both with and without the Chern-Simons term), (b) a recently proposed photonless gauge theory, and (c) a previously unknown model in which the parity-nonconserving term is associated with the (gauge-invariant) field strength rather than the gauge field itself. Some results for the commutation relations and propagators are given.
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