Abstract
We study the electrodynamics of generic charged particles (bosons, fermions, relativistic or not) constrained to move on an infinite plane. An effective gauge theory in (2 + 1)- dimensional space-time which describes the real electromagnetic interaction of these particles is obtained. The relationship between this effective theory with the Chern-Simons theory is explored. It is shown that the QED lagrangian per se produces the Chern-Simons constraint relating the current to the effective gauge field in 2 + 1 dimensions. It is also shown that the geometry of the system unavoidably induces a contribution from the topological θ- term that generates an explicit Chern-Simons term for the effective (2 + 1)-dimensional gauge field as well as a minimal coupling of the matter to it. The possible relation of the effective three-dimensional theory with the bosonization of the Dirac fermion field in 2 + 1 dimensions is briefly discussed as well as the potential applications in condensed matter systems.
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