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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 Duffin–Kemmer–Petiau algebra ： ウィキペディア英語版 Duffin–Kemmer–Petiau algebra In mathematical physics, the Duffin–Kemmer–Petiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the Duffin–Kemmer–Petiau matrices. These matrices form part of the Duffin–Kemmer–Petiau equation that provides a relativistic description of spin-0 and spin-1 particles. The DKP algebra is also referred to as the meson algebra.〔Jacques Helmstetter, Artibano Micali: ''About the Structure of Meson Algebras'', Advances in Applied Clifford Algebras, vol.&nbsnp;20, no. 3-4, pp. 617-629, , (abstract )〕 == Defining relations == The Duffin–Kemmer–Petiau matrices have the defining relation〔See introductory section of: Yu V. Pavlov: (''Duffin–Kemmer–Petiau equation with nonminimal coupling to curvature'' ), Gravitation & Cosmology, vol. 12 (2006), no.2–3, pp. 205–208〕 :$\backslash beta^\; \backslash beta^\; \backslash beta^\; +\; \backslash beta^\; \backslash beta^\; \backslash beta^\; =\; \backslash beta^\; \backslash eta^\; +\; \backslash beta^\; \backslash eta^$ where $\backslash eta^$ stand for a constant diagonal matrix. The Duffin–Kemmer–Petiau matrices $\backslash beta$ for which $\backslash eta^$ consists in diagonal elements (+1,-1,…,-1) form part of the Duffin–Kemmer–Petiau equation. Five-dimensional DKP matrices can be represented as:〔See for example I. Boztosun, M. Karakoc, F. Yasuk, A. Durmus: ''Asymptotic Iteration Method Solutions to the Relativistic Duffin-Kemmer-Petiau Equation'', Journal of Mathematical Physics vol. 47, 062301 (2006), , arXiv:math-ph/0604040v1 (submitted 18 April 2006) ()〕〔Anton Z. Capri: ''Relativistic quantum mechanics and introduction to quantum field theory'', World Scientific, 2002, ISBN 981-238-136-8, (p. 25 )〕 :$$ \beta^ = \begin 0&1&0&0&0\\ 1&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0 \end , $\backslash quad$ \beta^ = \begin 0&0&-1&0&0\\ 0&0&0&0&0\\ 1&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0 \end , $\backslash quad$ \beta^ = \begin 0&0&0&-1&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 1&0&0&0&0\\ 0&0&0&0&0 \end , $\backslash quad$ \beta^ = \begin 0&0&0&0&-1\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 1&0&0&0&0 \end These five-dimensional DKP matrices represent spin-0 particles. The DKP matrices for spin-1 particles are 10-dimensional.〔 The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spin‐0 and spin‐1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements.〔Ephraim Fischbach, Michael Martin Nieto, C. K. Scott: ''Duffin‐Kemmer‐Petiau subalgebras: Representations and applications'', Journal of Mathematical Physics, vol. 14, no. 12, 1760 (1973), ((abstract ))〕 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「Duffin–Kemmer–Petiau algebra」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.