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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 De Donder–Weyl theory ： ウィキペディア英語版 De Donder–Weyl theory In mathematical physics, the De Donder–Weyl theory is a formalism in the calculus of variations over spacetime which treats the space and time coordinates on equal footing. In this framework, a field is represented as a system that varies both in space and in time. = -\partial H / \partial y^ |- |$\backslash partial\; y^\; /\; \backslash partial\; x^\; =\; \backslash partial\; H\; /\; \backslash partial\; p^\_a$ |- |} == De Donder–Weyl formulation of field theory == The De Donder–Weyl theory is based on a change of variables. Let ''xi'' be spacetime coordinates, for ''i'' = 1 to ''n'' (with ''n'' = 4 representing 3 + 1 dimensions of space and time), and ''ya'' field variables, for ''a'' = 1 to ''m'', and ''L'' the Lagrangian density. :$L\; =\; L(y^,\backslash partial\_i\; y^,x^)$ With ''polymomenta'' ''pia'' defined as :$p^\_a\; =\; \backslash partial\; L\; /\; \backslash partial\; (\backslash partial\_i\; y^)$ and for ''De Donder–Weyl Hamiltonian function'' ''H'' defined as :$H\; =\; p^\_a\; \backslash partial\_i\; y^\; -\; L$ the De Donder–Weyl equations are:〔Igor V. Kanatchikov: (''Towards the Born–Weyl quantization of fields'' ), arXiv:quant-ph/9712058v1 (submitted on 31 December 1997)〕 :$\backslash partial\; p^\_a\; /\; \backslash partial\; x^\; =\; -\backslash partial\; H\; /\; \backslash partial\; y^\; \backslash ,\; ,\; \backslash ,\; \backslash partial\; y^\; /\; \backslash partial\; x^\; =\; \backslash partial\; H\; /\; \backslash partial\; p^\_a$ These canonical equations of motion are covariant. The theory is a formulation of a covariant Hamiltonian field theory and for ''n'' = 1 it reduces to Hamiltonian mechanics (see also action principle in the calculus of variations). The generalization of Poisson brackets to the De Donder–Weyl theory and the representation of De Donder-Weyl equations in terms of generalized Poisson brackets was found by Kanatchikov in 1993.〔Igor V. Kanatchikov: (''On the Canonical Structure of the De Donder-Weyl Covariant Hamiltonian Formulation of Field Theory I. Graded Poisson brackets and equations of motion'' ), arXiv:hep-th/9312162v1 (submitted on 20 Dec 1993)〕 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「De Donder–Weyl 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.