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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 Two-body Dirac equations ： ウィキペディア英語版 Two-body Dirac equations In quantum field theory, and in the significant subfields of quantum electrodynamics and quantum chromodynamics, the two-body Dirac equations (TBDE) of constraint dynamics provide a three-dimensional yet manifestly covariant reformulation of the Bethe–Salpeter equation for two spin-1/2 particles. Such a reformulation is necessary since without it, as shown by Nakanishi,〔N. Nakanishi, Supplement to Progress in Theoretical Physics 43 1, (1969)〕 the Bethe–Salpeter equation possesses negative-norm solutions arising from the presence of an essentially relativistic degree of freedom, the relative time. These "ghost" states have spoiled the naive interpretation of the Bethe–Salpeter equation as a quantum mechanical wave equation. The two-body Dirac equations of constraint dynamics rectify this flaw. The forms of these equations can not only be derived from quantum field theory 〔H. Sazdjian Physics Letters 156B, 381 (1985)〕〔H. Jallouli and H. Sazdjian, Annals of Physics, 253 , 376 (1997)〕 they can also be derived purely in the context of Dirac's constraint dynamics 〔P.A.M. Dirac, Canad. J. Math. 2, 129 (1950)〕〔P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964)〕 and relativistic mechanics and quantum mechanics.〔P. Van Alstine and H.W. Crater, Journal of Mathematical Physics 23, 1697 (1982).〕 Their structures, unlike the more familiar two-body Dirac equation of Breit,〔G. Breit, Physical Review 34, 553, (1929),36, 383, (1930) 39, 616, (1932)〕 which is a single equation, are that of two simultaneous quantum relativistic wave equations. A single two-body Dirac equation similar to the Breit equation can be derived from the TBDE.〔Peter Van Alstine and Horace W. Crater, "A tale of three equations: Breit, Eddington—Gaunt, and Two-Body Dirac" Foundations of Physics (27),67 (1997)〕 Unlike the Breit equation, it is manifestly covariant and free from the types of singularities that prevent a strictly nonperturbative treatment of the Breit equation.〔Horace W. Crater, Chun Wa Wong, and Cheuk-Yin Wong, International Journal of Modern Physics E Vol. 5 , 589 (1996)〕 In applications of the TBDE to QED, the two particles interact by way of four-vector potentials derived from the field theoretic electromagnetic interactions between the two particles. In applications to QCD, the two particles interact by way of four-vector potentials and Lorentz invariant scalar interactions, derived in part from the field theoretic chromomagnetic interactions between the quarks and in part by phenomenological considerations. As with the Breit equation a sixteen-component spinor Ψ is used. ==Equations== For QED, each equation has the same structure as the ordinary one-body Dirac equation in the presence of an external electromagnetic field, given by the 4-potential $A\_\backslash mu$. For QCD, each equation has the same structure as the ordinary one-body Dirac equation in the presence of an external field similar to the electromagnetic field and an additional external field given by in terms of a Lorentz invariant scalar $S$. In natural units:〔http://arxiv.org/pdf/hep-ph/9912386.pdf〕 those two-body equations have the form. :$((p\_1-\backslash tilde\_1)^\backslash mu+m\_1\; +\; \backslash tilde\_1)\backslash Psi=0,$ :$((p\_2-\backslash tilde\_2)^\backslash mu+m\_2\; +\; \backslash tilde\_2)\backslash Psi=0.$ where, in coordinate space, ''p''μ is the 4-momentum, related to the 4-gradient by (the metric used here is $\backslash eta\_=(-1,1,1,1)$) :$p^\backslash mu\; =\; -i$ and γμ are the gamma matrices. The two-body Dirac equations (TBDE) have the property that if one of the masses becomes very large, say $m\_\backslash rightarrow\; \backslash infty$ then the 16-component Dirac equation reduces to the 4-component one-body Dirac equation for particle one in an external potential. In SI units: :$((p\_1-\backslash tilde\_1)^\backslash mu+m\_1c\; +\; \backslash tilde\_1)\backslash Psi=0,$ :$((p\_2-\backslash tilde\_2)^\backslash mu+m\_2c\; +\; \backslash tilde\_2)\backslash Psi=0.$ where ''c'' is the speed of light and :$p^\backslash mu\; =\; -i\backslash hbar$ Natural units will be used below. A tilde symbol is used over the two sets of potentials to indicate that they may have additional gamma matrix dependencies not present in the one-body Dirac equation. Any coupling constants such as the electron charge are embodied in the vector potentials. 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「Two-body Dirac 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.