The relativistic non-Abelian Chern-Simons equations

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Abstract

We study the r × r system of nonlinear elliptic equations (formula presented) where λ > O is a constant parameter, K - (Kab) is the Cartan matrix of a semi-simple Lie algebra, and op is the Dirac measure concentrated at p ∈ R2. This system of equations arises in the relativistic non-Abelian Chern-Simons theory and may be viewed as a non-integrable deformation of the integrable Toda system. We establish the existence of a class of solutions known as topological multivortices. The crucial step in our method is the use of the decomposition theorem of Cholesky for positive definite matrices so that a variational principle can be formulated.

Original languageEnglish (US)
Pages (from-to)199-218
Number of pages20
JournalCommunications In Mathematical Physics
Volume186
Issue number1
DOIs
StatePublished - Jan 1 1997

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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