Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
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 -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.
Keywords
Cite
@article{arxiv.hep-th/9301034,
title = {Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory},
author = {E. C. Marino},
journal= {arXiv preprint arXiv:hep-th/9301034},
year = {2009}
}
Comments
Latex, 17 pages, 1 figure available from the author as a postscript file, preprint PUPT-1368