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Unformatted text preview: arXiv:hep-th/9511132v1 17 Nov 1995 Three-dimensional quantum electrodynamics as an effective interaction ∗ E. Abdalla † CERN, Theory Division, CH-1211 Geneva 23, Switzerland International Centre for Theoretical Physics - ICTP 34100 Trieste, Italy and F. M. de Carvalho Filho ‡ Center for Theoretical Physics Laboratory for Nuclear Science and Department of Physics Massachusetts Institute of Technology Cambridge, Massachusetts 02139 U.S.A. Abstract We obtain a Quantum Electrodynamics in 2+1 dimensions by applying a Kaluza–Klein type method of dimensional reduction to Quantum Electrodynamics in 3+1 dimensions rendering the model more realistic to application in solid-state systems, invariant under translations in one direction. We show that the model obtained leads to an effective action exhibiting an interesting phase structure and that the generated Chern–Simons term survives only in the broken phase. PACS number(s): 11.10.Kk, 12.20.-m, 73.40.Hm MIT–CTP–2488 IC/95/350 hep-th/9511132 November 1995 * This work is supported in part by funds provided by the U.S. Department of Energy(D.O.E.) under cooperative agreement #DF-FC02-94ER40818. † Email: firstname.lastname@example.org, email@example.com. Permanent address: Instituto de F´ ısica - USP, C.P. 20516, S. Paulo, Brazil. ‡ Email: firstname.lastname@example.org. Permanent Address: Instituto de Ciˆ encias, Escola Federal de En- genharia de Itajub´ a, C.P. 50, Itajub´ a, CEP: 375000-000, Minas Gerais, Brazil. 1. Introduction Models in (2+1) dimensions with or without Chern–Simons terms have been a subject of an intense theoretical study in the last years 1 − 9 , for several important reasons. First, they are generalizations of two-dimensional models 10 , where one can have an interesting theoretical laboratory for check of ideas, a little more complex than the two-dimensional case, but still without all the technical complexity of four dimensions. This is the case of the gravitation theory in (2+1) dimensions 1 that is very simple from the classical point of view: it has zero degrees of freedom, but topological effects appear, and are effective to the understanding of the physics involved. Another equally important to study such models, is that they can be useful in determining properties of certain important practical condensed-matter systems. In particular many efforts have been recently devoted to find good theoretical explanations for the high-T c superconductivity 6 − 9 , 11 , 12 as well as for the fractional quantum Hall effect 13 which are observed in some layered ceramics. These materials exhibit a planar geometry that can, in principle, be described by models in quantum field theory with only two spatial coordinates. So one of the main challenges in this area is to find correct models for description of these phenomena....
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