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Vortex Condensates for Relativistic Abelian Chern-Simons Model with Two Higgs Scalar Fields and Two Gauge Fields on a Torus

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Abstract

We prove the existence of maximal condensates for the relativistic Abelian Chern-Simons equations involving two Higgs particles and two gauge fields on a torus. After a change of variable, we obtain a variational formulation of the problem whose critical points are equivalent to the original system of the equation. We prove existence of a local minimizer for this functional as well as the existence of a second mountain-pass critical point.

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Authors and Affiliations

  1. Department of Mathematics, Taida Institute of Mathematical Sciences,, National Taiwan University, Taipei, 106, Taiwan

    Chang-Shou Lin

  2. Department of Mathematics, Arts and Science Program, The Petroleum Institute, Abu Dhabi, P.O. 2533, U.A.E

    Jyotshana V. Prajapat

Authors
  1. Chang-Shou Lin
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  2. Jyotshana V. Prajapat
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Correspondence to Jyotshana V. Prajapat.

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Communicated by I.M. Sigal

Dedicated to Professor Louis Nirenberg

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Lin, CS., Prajapat, J.V. Vortex Condensates for Relativistic Abelian Chern-Simons Model with Two Higgs Scalar Fields and Two Gauge Fields on a Torus. Commun. Math. Phys. 288, 311–347 (2009). https://doi.org/10.1007/s00220-009-0774-8

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  • DOI: https://doi.org/10.1007/s00220-009-0774-8

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