Study of the "Non-Abelian" Current Algebra of a Non-linear $σ$-Model

Details Study of the "Non-Abelian" Current Algebra of a Non-linear $σ$-Model Study of the "Non-Abelian" Current Algebra of a Non-linear $σ$-Model

2006-03-16

arxiv.org/abs/hep-th/0603128v2

Physics

High Energy Physics

High Energy Physics - Theory

Revised version, To appear in Phys.Lett.B

Scientific paper

10.1016/j.physletb.2006.07.032

A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure functions}}. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in \cite{car}. The connection with noncommutative geometry is also established.

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