Gauge theories in three-dimensional space-time

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Abstract
The most general Abelian gauge theory in two spatial dimensions is constructed in accordance with a few precisely formulated principles. It is found that there exists an additional parameter in the theory which essentially arises from the inclusion of a kinematical term involving only the dual of the gauge-invariant field tensor. The Lagrangian and field equations are displayed in different forms which are useful according to the particular value of the new parameter λ. Commutation relations in the radiation gauge as well as the free photon propagator are derived. The latter is used to calculate in perturbation theory the fermion self-energy and to search for a bound-state photon.

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