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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 Chiral anomaly ： ウィキペディア英語版 Chiral anomaly In physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In some theories of fermions with chiral symmetry, the quantization may lead to the breaking of this (global) chiral symmetry. In that case, the charge associated with the chiral symmetry is not conserved. The non-conservation happens in a tunneling process from one vacuum to another. Such a process is called an instanton. In the case of a symmetry related to the conservation of a fermionic particle number, one may understand the creation of such particles as follows. The definition of a particle is different in the two vacuum states between which the tunneling occurs; therefore a state of no particles in one vacuum corresponds to a state with some particles in the other vacuum. In particular, there is a Dirac sea of fermions and, when such a tunneling happens, it causes the energy levels of the sea fermions to gradually shift upwards for the particles and downwards for the anti-particles, or vice versa. This means particles which once belonged to the Dirac sea become real (positive energy) particles and particle creation happens. Technically, an anomalous symmetry is a symmetry of the action $\backslash mathcal\; A$, but not of the measure $\backslash ,\backslash mu$, and therefore ''not'' of the generating functional $\backslash mathcal\; Z=\backslash int$ of the quantized theory ($\backslash hbar$ is Planck's action-quantum divided by $2\backslash pi$). The measure consists of a part depending on the fermion field $\backslash !\; d\backslash psi$ and a part depending on its complex conjugate $d\backslash bar$. The transformations of both parts under a chiral symmetry do not cancel in general. Note that if $\backslash !\; \backslash psi$ is a Dirac fermion, then the chiral symmetry can be written as $\backslash psi\; \backslash rightarrow\; e^\backslash psi$ where $\backslash !\; \backslash alpha$ is some matrix acting on $\backslash !\; \backslash psi$. From the formula for $\backslash mathcal\; Z$ one also sees explicitly that in the classical limit, $\backslash hbar\; \backslash to\; 0,$ anomalies don't come into play, since in this limit only the extrema of $\backslash mathcal\; A$ are relevant. The anomaly is in fact proportional to the instanton number of a gauge field to which the fermions are coupled (note that the gauge symmetry is always non-anomalous and is exactly respected, as is required by the consistency of the theory). ==Calculation== The chiral anomaly can be calculated exactly by one-loop Feynman diagrams, e.g. the famous "triangle diagram", contributing to the pion decays, $\backslash pi^0\; \backslash to\backslash gamma\backslash gamma$ and $\backslash pi^0\backslash to\; e^+e^-\backslash gamma$. The amplitude for this process can be calculated directly from the change in the measure of the fermionic fields under the chiral transformation. Wess and Zumino developed a set of conditions on how the partition function ought to behave under gauge transformations called the Wess-Zumino consistency conditions. Fujikawa derived this anomaly using the correspondence between functional determinants and the partition function using the Atiyah-Singer index theorem. See Fujikawa's method. 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「Chiral anomaly」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.