The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory

Details The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory

1995-11-26

arxiv.org/abs/hep-th/9511184v1

J.Math.Phys. 37 (1996) 4368-4387

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, Plain Tex

Scientific paper

10.1063/1.531636

We show that the Nonlinear Schr\"odinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and the Inverse Spectral Transform, has appear as a homogeneous part (condensate) of the statistical gauge field, connected with the compactified extra space coordinate. In terms of solitons, a natural interpretation for the one-dimensional analog of Chern-Simons Gauss law is given.

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