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
StatePublished - 1997

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Cartan Matrix
Cholesky
Chern-Simons Theories
Semisimple Lie Algebra
Positive definite matrix
Nonlinear Elliptic Equations
Decomposition Theorem
variational principles
matrices
Variational Principle
Paul Adrien Maurice Dirac
System of equations
algebra
theorems
decomposition
Class

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

The relativistic non-Abelian Chern-Simons equations. / Yang, Yisong.

In: Communications in Mathematical Physics, Vol. 186, No. 1, 1997, p. 199-218.

Research output: Contribution to journalArticle

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