Toda field theory

In the study of field theory and partial differential equations, a Toda field theory (named after Morikazu Toda) is derived from the following Lagrangian:

Here x and t are spacetime coordinates, (,) is the Killing form of a real r-dimensional Cartan algebra ${\displaystyle {\mathfrak {h}}}$ of a Kac–Moody algebra over ${\displaystyle {\mathfrak {h}}}$, α_i is the i^thsimple 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.

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