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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 Spectral asymmetry ： ウィキペディア英語版 Spectral asymmetry In mathematics and physics, the spectral asymmetry is the asymmetry in the distribution of the spectrum of eigenvalues of an operator. In mathematics, the spectral asymmetry arises in the study of elliptic operators on compact manifolds, and is given a deep meaning by the Atiyah-Singer index theorem. In physics, it has numerous applications, typically resulting in a fractional charge due to the asymmetry of the spectrum of a Dirac operator. For example, the vacuum expectation value of the baryon number is given by the spectral asymmetry of the Hamiltonian operator. The spectral asymmetry of the confined quark fields is an important property of the chiral bag model. ==Definition== Given an operator with eigenvalues $\backslash omega\_n$, an equal number of which are positive and negative, the spectral asymmetry may be defined as the sum :$B=\backslash lim\_\; \backslash frac\backslash sum\_n\; \backslash sgn(\backslash omega\_n)\; \backslash exp\; -t|\backslash omega\_n|$ where $\backslash sgn(x)$ is the sign function. Other regulators, such as the zeta function regulator, may be used. The need for both a positive and negative spectrum in the definition is why the spectral asymmetry usually occurs in the study of Dirac operators. 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「Spectral asymmetry」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.