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

Subir Ghosh
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Abstract

A particular form of non-linear $σ$-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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Subir Ghosh. 2006-07-16. Study of the "Non-Abelian" Current Algebra of a Non-linear $σ$-Model. https://doi.org/10.1016/j.physletb.2006.07.032

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