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arXiv · 1301.7483

An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system

Paul Smith
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Abstract

We consider energy-critical Schrödinger maps from R^2 into the sphere and hyperbolic plane. Viewing such maps with respect to orthonormal frames on the pullback bundle provides a gauge field formulation of the evolution. We show that this gauge field system is the set of Euler-Lagrange equations corresponding to an action that includes a Chern-Simons term. We also introduce the stress-energy tensor and derive conservation laws. In conclusion we offer comparisons between Schrödinger maps and the closely related Chern-Simons-Schrödinger system.

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Paul Smith. 2014-04-14. An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system. https://arxiv.org/abs/1301.7483

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