Chern—Simons Systems: Abelian Case

  • Yisong Yang
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

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.

Keywords

Maximum Principle Maximal Solution Periodic Domain Vortex Solution Abelian Higgs Model 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Yisong Yang
    • 1
  1. 1.Department of Applied Mathematics and PhysicsPolytechnic UniversityBrooklynUSA

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