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A New Approach to Integrable Theories in any Dimension

Orlando Alvarez·Luiz A. Ferreira·J. Sanchez Guillen
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Abstract

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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Orlando Alvarez, Luiz A. Ferreira, J. Sanchez Guillen. 1998-05-19. A New Approach to Integrable Theories in any Dimension. https://doi.org/10.1016/s0550-3213(98)00400-3

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