Toda Field Theory
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High Quality Content by WIKIPEDIA articles! In the study of field theory and partial differential equations, a Toda field theory is derived from the following Lagrangian: mathcal{L}=frac{1}{2}left[left({partial phi over partial t},{partial phi over partial t}right)-left({partial phi over partial x}, {partial phi over partial x}right)right ]-{m^2 over beta^2}sum_{i=1}^r n_i e^{beta alpha_i cdot phi}.Here x and t are spacetime coordinates, (,) is the Killing form of a real r-dimensional Cartan algebra mathfrak{h} of a Kac-Moody algebra over mathfrak{h}, i is the ith simple root in some root basi...
High Quality Content by WIKIPEDIA articles! In the study of field theory and partial differential equations, a Toda field theory is derived from the following Lagrangian: mathcal{L}=frac{1}{2}left[left({partial phi over partial t},{partial phi over partial t}right)-left({partial phi over partial x}, {partial phi over partial x}right)right ]-{m^2 over beta^2}sum_{i=1}^r n_i e^{beta alpha_i cdot phi}.Here x and t are spacetime coordinates, (,) is the Killing form of a real r-dimensional Cartan algebra mathfrak{h} of a Kac-Moody algebra over mathfrak{h}, i is the ith simple root in some root basis, ni is the Coxeter number, m is the mass (or bare mass in the quantum field theory version) and is the coupling constant.Then a Toda field theory is the study of a function mapping 2 dimensional Minkowski space satisfying the corresponding Euler-Lagrange equations.If the Kac-Moody 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 which decouples is removed) and if it is hyperbolic, it is called a hyperbolic Toda field theory.
