Integrability in theories with local U(1) gauge symmetry

@article{Adam2007IntegrabilityIT,
  title={Integrability in theories with local U(1) gauge symmetry},
  author={Christoph Adam and Joaquin Sanchez-Guillen and Andrzej Wereszczynski},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2007},
  volume={40},
  pages={9079 - 9088}
}
Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1… 
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5 Citations

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References

SHOWING 1-10 OF 37 REFERENCES

Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target…

A new approach to integrable theories in any dimension

Integrable chiral theories in 2 + 1 dimensions

New integrable sectors in the Skyrme and four-dimensional CPn models

The application of a weak integrability concept to the Skyrme and CPn models in four dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic…

Conservation laws in Skyrme-type models

The zero curvature representation of Zakharov and Shabat [V. E. Zakharov and A. B. Shabat, Soviet Phys. JETP 34, 62 (1972)] has been generalized recently to higher dimensions and has been used to…

Bogomol'nyi equations of Chern-Simons Higgs theory from a generalized abelian Higgs model

Bogomol'nyi solitons in a gauged $O(3)$ sigma model

Infinite symmetries in the Skyrme model

Integrability from an Abelian Subgroup of the diffeomorphisms group

It has been known for some time that for a large class of nonlinear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with…

Dynamics of Abelian Higgs vortices in the near Bogomolny regime

The aim of this paper is to give an analytical discussion of the dynamics of the Abelian Higgs multi-vortices whose existence was proved by Taubes ([JT82]). For a particular value of a parameter of…