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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Toda field theory ： ウィキペディア英語版 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: :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 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 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 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. ==Examples== Liouville field theory is associated to the A1 Cartan matrix. The sinh-Gordon 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 sine-Gordon model is the model with the same Cartan matrix but an imaginary β. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Toda field theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.