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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 Helicity basis ： ウィキペディア英語版 Helicity basis In the Standard Model, using quantum field theory it is conventional to use the helicity basis to simplify calculations (of cross sections, for example). In this basis, the spin is quantized along the axis in the direction of motion of the particle. ==Spinors== The two-component helicity eigenstates $\backslash xi\_\backslash lambda$ satisfy ::$\backslash sigma\; \backslash cdot\; \backslash hat\; \backslash xi\_\backslash lambda(\backslash hat)=\backslash lambda\; \backslash xi\_\backslash lambda(\backslash hat)\; \backslash ,$ :where :$\backslash sigma\; \backslash ,$ are the Pauli matrices, :$\backslash hat\; \backslash ,$ is the direction of the fermion momentum, :$\backslash lambda\; =\; \backslash pm\; 1\; \backslash ,$ depending on whether spin is pointing in the same direction as $\backslash hat\; \backslash ,$ or opposite. To say more about the state, $\backslash xi\_\backslash lambda\; \backslash ,$ we will use the generic form of fermion four-momentum: ::$p^\backslash mu=\; \backslash left(E,\; |\backslash vec|\; \backslash sin\; \backslash cos,\; |\backslash vec|\; \backslash sin\; \backslash sin,\; |\backslash vec|\; \backslash cos\; \backslash right)\; \backslash ,$ Then one can say the two helicity eigenstates are ::$\backslash xi\_(\backslash vec)$ = \frac| + p_z)}} \begin |\vec|+p_z\\ p_x+i p_y \end = \begin \cos}\\ e^\sin} \end\, and ::$\backslash xi\_(\backslash vec)$ = \frac| + p_z)}} \begin -p_x+i p_y\\ |\vec|+p_z \end = \begin -e^\sin}\\ \cos} \end\, These can be simplified by defining the z-axis such that the momentum direction is either parallel or anti-parallel, or rather: ::$\backslash hat\; =\; \backslash pm\; \backslash hat\; \backslash ,$. In this situation the helicity eigenstates are for when the particle momentum is $\backslash hat\; =\; +\; \backslash hat\; \backslash ,$ ::$\backslash xi\_(\backslash hat)\; =\; \backslash begin$ 1\\ 0 \end \, and $\backslash xi\_(\backslash hat)\; =\; \backslash begin$ 0\\ 1 \end \, for then for when momentum is $\backslash hat\; =\; -\; \backslash hat\; \backslash ,$ ::$\backslash xi\_(-\backslash hat)\; =\; \backslash begin$ 0\\ 1 \end \, and $\backslash xi\_(-\backslash hat)\; =\; \backslash begin$ -1\\ 0 \end \, 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「Helicity basis」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.