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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 Mass gap ： ウィキペディア英語版 Mass gap In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. Since exact energy eigenstates are infinitely spread out and are therefore usually excluded from a formal mathematical description, a stronger definition is that the mass gap is the greatest lower bound of the energy of any state which is orthogonal to the vacuum. ==Mathematical definitions== For a given real field $\backslash phi(x)$, we can say that the theory has a mass gap if the two-point function has the property :$\backslash langle\backslash phi(0,t)\backslash phi(0,0)\backslash rangle\backslash sim\; \backslash sum\_nA\_n\backslash exp\backslash left(-\backslash Delta\_nt\backslash right)$ with $\backslash Delta\_0>0$ being the lowest energy value in the spectrum of the Hamiltonian and thus the mass gap. This quantity, easy to generalize to other fields, is what is generally measured in lattice computations. It was proved in this way that Yang–Mills theory develops a mass gap on a lattice.〔.〕〔.〕 The corresponding time-ordered value, the propagator, will have the property :$\backslash lim\_\backslash Delta(p)=\backslash mathrm$ with the constant being finite. A typical example is offered by a free massive particle and, in this case, the constant has the value 1/''m''2. In the same limit, the propagator for a massless particle is singular. 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「Mass gap」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.