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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 Schwinger's quantum action principle ： ウィキペディア英語版 Schwinger's quantum action principle Schwinger's quantum action principle is a variational approach to quantum field theory introduced by Julian Schwinger. In this approach, the quantum action is an operator. Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical. Suppose we have two states defined by the values of a complete set of commuting operators at two times. Let the early and late states be $|\; A\; \backslash rang$ and $|\; B\; \backslash rang$, respectively. Suppose that there is a parameter in the Lagrangian which can be varied, usually a source for a field. The main equation of Schwinger's quantum action principle is: :$\backslash delta\; \backslash langle\; B|A\backslash rangle\; =\; i\; \backslash langle\; B|\; \backslash delta\; S\; |A\backslash rangle,\backslash$ where the derivative is with respect to small changes in the parameter. In the path integral formulation, the transition amplitude is represented by the sum over all histories of $\backslash exp(iS)$, with appropriate boundary conditions representing the states $|\; A\; \backslash rang$ and $|\; B\; \backslash rang$. The infinitesimal change in the amplitude is clearly given by Schwinger's formula. Conversely, starting from Schwinger's formula, it is easy to show that the fields obey canonical commutation relations and the classical equations of motion, and so have a path integral representation. Schwinger's formulation was most significant because it could treat fermionic anticommuting fields with the same formalism as bose fields, thus implicitly introducing differentiation and integration with respect to anti-commuting coordinates. ==External links== *() A brief (but very technical) description of Schwinger's paper 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「Schwinger's quantum action principle」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.