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A New Approach to Integrable Theories in any Dimension

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arxiv hep-th/9710147 v2 pith:DTCO36TB submitted 1997-10-18 hep-th nlin.SIsolv-int

Orlando Alvarez , Luiz A. Ferreira , J. Sanchez Guillen This is my paper · ORCID
classification hep-thnlin.SIsolv-int
keywords conservedcurrentstheoriesapproachconstructcurvaturedimensiondimensional
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The zero curvature representation for two dimensional integrable models is generalized to spacetimes of dimension d+1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2+1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the CP^1 model) and 3+1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2+1 dimensional CP^1 model, we explicitly construct an infinite number of previously unknown nontrivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j+1 conserved currents leading to 2j+1 Lorentz scalar charges.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Symmetry TFTs for Continuous Spacetime Symmetries

    hep-th 2025-09 conditional novelty 7.0 of 10

    Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.

  2. Signum-Gordon spectral mass from nonlinear Fourier mode mixing

    hep-th 2026-02 unverdicted novelty 6.0 of 10

    A specific initial amplitude in the signum-Gordon model generates a spectral mass of unity whose dispersion matches the massive Klein-Gordon equation.

  3. On the gauge-invariant dynamical charges and densities of the 1-instanton solution

    hep-th 2026-06 unverdicted novelty 4.0 of 10

    Gauge-invariant charge densities for the 1-instanton are defined via non-Abelian magnetic and electric fluxes through spheres, yielding non-zero values at r=1 for both instanton and anti-instanton.

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