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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 Variational perturbation theory ： ウィキペディア英語版 Variational perturbation theory In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say :$s=\backslash sum\_^\backslash infty\; a\_n\; g^n$, into a convergent series in powers :$s=\backslash sum\_^\backslash infty\; b\_n\; /(g^\backslash omega)^n$, where $\backslash omega$ is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner). This is possible with the help of variational parameters, which are determined by optimization order by order in $g$. The partial sums are converted to convergent partial sums by a method developed in 1992.〔 〕 Most perturbation expansions in quantum mechanics are divergent for any small coupling strength $g$. They can be made convergent by VPT (for details see the first textbook cited below). The convergence is exponentially fast.〔 〕〔 〕 After its success in quantum mechanics, VPT has been developed further to become an important mathematical tool in quantum field theory with its anomalous dimensions.〔 〕 Applications focus on the theory of critical phenomena. It has led to the most accurate predictions of critical exponents. More details can be read (here ). == References == 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「Variational perturbation 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.