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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 Bargmann–Wigner equations ： ウィキペディア英語版 Bargmann–Wigner equations :''This article uses the Einstein summation convention for tensor/spinor indices, and uses hats for quantum operators. In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations (or BW equations or BWE) are relativistic wave equations which describe free particles of arbitrary spin , an integer for bosons () or half-integer for fermions (). The solutions to the equations are wavefunctions, mathematically in the form of multi-component spinor fields. The spin quantum number is usually denoted by in quantum mechanics, however in this context is more typical in the literature (see references). They were proposed by Valentine Bargmann and Eugene Wigner in 1948, using Lorentz group theory, and building on the work of those who pioneered quantum theory within the first half of the twentieth century.〔 NB: The convention for the four gradient in this article is , same as the Wikipedia article. Jeffery's conventions are different: . Also Jeffery uses collects the and components of the momentum operator: . The components are not to be confused with ladder operators; the factors of occur from the gamma matrices.〕 ==Origin from the Dirac equation== (詳細はcovariant form of the Dirac equation for an uncharged particle is: where is a rank-1 4-component spinor field, a function of the particle's position and time , with components in which is a bispinor index that takes values 1, 2, 3, 4. Further, are the gamma matrices, and :$\backslash hat\_\backslash mu\; =\; i\backslash hbar\; \backslash partial\_\backslash mu$ is the 4-momentum operator. The operator constituting the entire equation, , is a matrix, because of the matrices, and the term scalar-multiplies the identity matrix (usually not written for simplicity). Explicitly, in the Dirac representation of the gamma matrices:〔 :$$ \begin -\gamma^\mu \hat_\mu + mc & = -\gamma^0 \frac - \boldsymbol\cdot(-\hat I_2 & 0 \\ 0 & -I_2 \\ \end\frac + \begin 0 & \boldsymbol\cdot\hat\cdot\hat + \begin I_2 & 0 \\ 0 & I_2 \\ \endmc \\ & = \begin -\hat/c+mc & 0 & \hat_z & \hat_x - i\hat_y \\ 0 & -\hat/c+mc & \hat_x + \hat_y & -\hat_z \\ -\hat_z & -(\hat_x - i\hat_y) & \hat/c+mc & 0 \\ -(\hat_x + i\hat_y) & \hat_z & 0 & \hat/c+mc \\ \end \end where is a vector of the Pauli matrices, ''E'' is the energy operator, is the 3-momentum operator, denotes the identity matrix, the zeros (in the second line) are actually blocks of zero matrices. The Dirac equation () can be written as a coupled set of equations: )\psi_ |}} )\psi_ |}} where :$\backslash Psi\; =$ \begin \psi_ \\ \psi_ \\ \end\,\quad \psi_ = \begin \psi_1 \\ \psi_2 \\ \end\,\quad \psi_ = \begin \psi_3 \\ \psi_4 \\ \end\,. One 2-component spinor describes the spin-1/2 fermion, the other describes the antifermion. For a charged particle moving in an electromagnetic field, minimal coupling can be introduced: where is the electric charge of the particle and is the electromagnetic four-potential. 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「Bargmann–Wigner equations」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.