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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 Gopakumar–Vafa invariant ： ウィキペディア英語版 Gopakumar–Vafa invariant In theoretical physics Rajesh Gopakumar and Cumrun Vafa introduced new topological invariants, which named Gopakumar–Vafa invariant, that represent the number of BPS states on Calabi–Yau 3-fold, in a series of papers. (see , and also see , .)　They lead the following formula generating function for the Gromov–Witten invariant on Calabi–Yau 3-fold ''M''. :$\backslash sum\_\; GW(g,\backslash beta)q^\backslash lambda^=\backslash sum\_BPS(r,\backslash beta)\backslash frac\backslash left(2\backslash sin\backslash left(\backslash frac\backslash right)^q^\backslash right)$ where $GW(g,\backslash beta)$ is Gromov–Witten invariant, $\backslash beta$ the number of pseudoholomorphic curves with genus ''g'' and $BPS(r,\backslash beta)$ the number of the BPS states. == As a partition function in topological quantum field theory == Gopakumar–Vafa invariants can be viewed as a partition function in topological quantum field theory.　They are proposed to be the partition function in Gopakumar–Vafa form: :$Z\_=\backslash exp\backslash left(k>0,\backslash \; r\backslash ge0,\backslash \backslash \; \backslash beta\backslash in\; H^2(M,\backslash mathbb)\backslash end\}BPS(r,\backslash beta)\backslash frac\backslash left(2\backslash sin\backslash left(\backslash frac\backslash right)^q^\backslash right)\backslash right)\backslash \; .$ 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「Gopakumar–Vafa invariant」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.