翻訳と辞書 Words near each other ・ Quartetto dell’Arte (String Quartet) ・ Quartetto di Cremona ・ Quartetto Egie ・ Quartetto Energie Nove ・ Quartetto Gelato ・ Quartetto Italiano ・ Quartetto Ritmo ・ Quartettsatz ・ Quartettsatz, D 103 (Schubert) ・ Quartettsatz, D 703 (Schubert) ・ Quartey ・ Quarth ・ Quartic ・ Quartic function ・ Quartic graph ・ Quartic interaction ・ Quartic plane curve ・ Quartic reciprocity ・ Quartic surface ・ Quartic threefold ・ Quartier Asiatique ・ Quartier Captaine Danjou ・ Quartier Concordia ・ Quartier de La Chapelle ・ Quartier des Grandes-Carrières ・ Quartier des spectacles ・ Quartier DIX30 ・ Quartier du Faubourg-du-Roule ・ Quartier du Roi ・ Quartier Général d'Aboville Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quartic interaction ： ウィキペディア英語版 Quartic interaction This article refers to a type of self-interaction in scalar field theory, a topic in quantum field theory. Other types of quartic interactions may be found under the topic of four-fermion interactions. A classical free scalar field $\backslash varphi$ satisfies the Klein–Gordon equation. If a scalar field is denoted $\backslash varphi$, a quartic interaction is represented by adding a potential term $\backslash frac\; \backslash varphi^4$. The coupling constant $\backslash lambda$ is dimensionless in 4-dimensional space-time. This article uses the (+−−−) metric signature for Minkowski space. ==The Lagrangian== The Lagrangian for a real scalar field with a quartic interaction is :$\backslash mathcal(\backslash varphi)=\backslash frac\; (\backslash varphi\; \backslash partial\_\backslash mu\; \backslash varphi\; -m^2\; \backslash varphi^2)\; -\backslash frac\backslash lambda\; \backslash varphi^4.$ This Lagrangian has a global Z2 symmetry mapping $\backslash varphi$ to $-\backslash varphi$. For ''two'' scalar fields $\backslash varphi\_1$ and $\backslash varphi\_2$ the Lagrangian has the form :$\backslash mathcal(\backslash varphi\_1,\backslash varphi\_2)\; =$ \frac (\partial_\mu \varphi_1 \partial^\mu \varphi_1 - m^2 \varphi_1^2 ) + \frac (\partial_\mu \varphi_2 \partial^\mu \varphi_2 - m^2 \varphi_2^2 ) - \frac \lambda (\varphi_1^2 + \varphi_2^2)^2, which can be written more concisely introducing a complex scalar field $\backslash phi$ defined as :$\backslash phi\; \backslash equiv\; \backslash frac(\backslash phi)=\backslash partial^\backslash mu\; \backslash phi^$ * \partial_\mu \phi -m^2 \phi^ * \phi -\lambda (\phi^ * \phi)^2, which is thus equivalent to the SO(2) model of real scalar fields $\backslash varphi\_1,\; \backslash varphi\_2$, as can be seen expanding the complex field $\backslash phi$ in real and imaginary parts. With $N$ real scalar fields, we can have a $\backslash varphi^4$ model with a global SO(N) symmetry given by the Lagrangian :$\backslash mathcal(\backslash varphi\_1,...,\backslash varphi\_N)=\backslash frac\; (\backslash varphi\_a\; \backslash partial\_\backslash mu\; \backslash varphi\_a\; -\; m^2\; \backslash varphi\_a\; \backslash varphi\_a)\; -\backslash frac\; \backslash lambda\; (\backslash varphi\_a\; \backslash varphi\_a)^2,\; \backslash quad\; a=1,...,N.$ Expanding the complex field in real and imaginary parts shows that it is equivalent to the SO(2) model of real scalar fields. In all of the models above, the coupling constant $\backslash lambda$ must be positive, since, otherwise, the potential would be unbounded below, and there would be no stable vacuum. Also, the Feynman path integral discussed below would be ill-defined. In 4 dimensions, $\backslash phi^4$ theories have a Landau pole. This means that without a cut-off on the high-energy scale, renormalization would render the theory trivial. 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「Quartic interaction」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.