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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 bispinor ： ウィキペディア英語版 bispinor In physics, a bispinor is an object with four complex components which transform in a specific way under Lorentz transformations: specifically, a bispinor is an element of a 4-dimensional complex vector space considered as a (½,0)⊕(0,½) representation of the Lorentz group.〔Caban and Rembielinski 2005, p. 2.〕 Bispinors are, for example, used to describe relativistic spin-½ wave functions. In the Weyl basis, a bispinor :$\backslash psi=\backslash left(\backslash begin\backslash psi\_L\backslash \backslash \; \backslash psi\_R\backslash end\backslash right)$ consists of two (two-component) Weyl spinors $\backslash psi\_L$ and $\backslash psi\_R$ which transform, correspondingly, under (½,0) and (0,½) representations of the $SO(1,3)$ group (the Lorentz group without parity transformations). Under parity transformation the Weyl spinors transform into each other. The Dirac bispinor is connected with the Weyl bispinor by a unitary transformation to the Dirac basis, :$$ \psi\rightarrow\left()\psi= \left(\begin\psi_R+\psi_L\\ \psi_R-\psi_L \end\right) . The Dirac basis is the one most widely used in the literature. ==Expressions for Lorentz transformations of bispinors== A bispinor field $\backslash psi(x)$ transforms according to the rule :$\backslash psi^a(x)\; \backslash to\; ^a(x^\backslash prime)\; =\; S()^a\_b\; \backslash psi^b(\backslash Lambda^x^\backslash prime)\; =\; S()^a\_b\; \backslash psi^b(x)$ where $\backslash Lambda$ is a Lorentz transformation. Here the coordinates of physical points are transformed according to $x^\backslash prime\; =\; \backslash Lambda\; x$, while $S$, a matrix, is an element of the spinor representation (for spin ) of the Lorentz group. In the Weyl basis, explicit transformation matrices for a boost $\backslash Lambda\_$ and for a rotation $\backslash Lambda\_$ are the following:〔David Tong, (''Lectures on Quantum Field Theory'' ) (2012), Lecture 4〕 :$S()\; =\; \backslash left($ \begin e^&0\\ 0&e^ \end \right) :$S()\; =\; \backslash left($ \begin e^&0\\ 0&e^ \end \right) Here $\backslash chi$ is the boost parameter, and $\backslash phi^i$ represents rotation around the $x^i$ axis. $\backslash sigma\_i$ are the Pauli matrices. The exponential is the exponential map, in this case the matrix exponential defined by putting the matrix into the usual power series for the exponential function. 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「bispinor」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.