Study of the "Non-Abelian" Current Algebra of a Non-linear σ-Model
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 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 car. The connection with noncommutative geometry is also established.
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