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arXiv · hep-th/9301034

Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory

E. C. Marino
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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 spacetime which describes the real electromagnetic interaction of this particles is obtained. The relationship between this effective theory with the Chern-Simons theory is explored. It is shown that the QED lagrangian {\it per se} produces the Chern-Simons constraint relating the current to the effective gauge field in 2+1 D. 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 D is briefly discussed as well as the potential applications in Condensed Matter systems.

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E. C. Marino. 1993-01-11. Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory. https://doi.org/10.1016/0550-3213(93)90379-4

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