Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-10-18
Nucl.Phys. B529 (1998) 689-736
Physics
High Energy Physics
High Energy Physics - Theory
52 pages, 4 figures, shortened version to appear in NPB
Scientific paper
10.1016/S0550-3213(98)00400-3
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.
Alvarez Orlando
Ferreira Luiz A.
Guillen Joaquin Sanchez
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