Chern—Simons Systems: Abelian Case
In this chapter we present a study of an important planar Abelian gauge field theory arising in condensed matter physics in which electromagnetism is governed by a Chern—Simons dynamics. In §5.1 we consider the gauged Schrödinger equation, which is nonrelativistic, and we present its explicit solution. In §5.2 we introduce the relativistic Chern—Simons model and state our main results concerning its topological solutions. In §5.3 we make a systematic analysis of the problem and prove the existence theorem stated in §5.2. In §5.4 we obtain all possible symmetric non-topological solutions. In §5.5 and §5.6 we construct spatially periodic solutions modelling a condensed lattice structure.
KeywordsVortex Soliton Lution Topo Electromagnetism
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