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Toda field theoryIn the study of field theory and partial differential equations, a Toda field theory is derived from the following Lagrangian: Additional recommended knowledgeHere x and t are spacetime coordinates, (,) is the Killing form of a real rdimensional Cartan algebra of a KacMoody algebra over , α_{i} is the i^{th} simple root in some root basis, n_{i} is the Coxeter number, m is the mass (or bare mass in the quantum field theory version) and β is the coupling constant. Then a Toda field theory is the study of a function φ mapping 2 dimensional Minkowski space satisfying the corresponding EulerLagrange equations. If the KacMoody algebra is finite, it's called a Toda field theory. If it is affine, it is called an affine Toda field theory (after the component of φ which decouples is removed) and if it is hyperbolic, it is called a hyperbolic Toda field theory. Toda field theories are integrable models and their solutions describe solitons. The sinhGordon model is the affine Toda field theory with the generalized Cartan matrix and a positive value for β after we project out a component of φ which decouples. The sineGordon model is the model with the same Cartan matrix but an imaginary β. References

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Toda_field_theory". A list of authors is available in Wikipedia. 